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Flashcard 1731683028236

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#dynamic-programming
Question
In dynamic programming each of the subproblem solutions is [...], typically based on the values of its input parameters, so as to facilitate its lookup.
Answer
indexed in some way


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occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time at the expense of a (hopefully) modest expenditure in storage space. (Each of the subproblem solutions is <span>indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup.) <span><body><html>

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Dynamic programming - Wikipedia
This article's factual accuracy is disputed. Relevant discussion may be found on the talk page. Please help to ensure that disputed statements are reliably sourced. (November 2015) (Learn how and when to remove this template message) <span>In computer science, mathematics, management science, economics and bioinformatics, dynamic programming (also known as dynamic optimization) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions. The next time the same subproblem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time at the expense of a (hopefully) modest expenditure in storage space. (Each of the subproblem solutions is indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup.) The technique of storing solutions to subproblems instead of recomputing them is called "memoization". Dynamic programming algorithms are often used for optimization. A dyna







Flashcard 1731703737612

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#finance
Question
The Black–Scholes model is a mathematical model of a financial market containing [...] instruments
Answer
derivative investment


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The Black–Scholes / ˌ b l æ k ˈ ʃ oʊ l z / [1] or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of E

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Black–Scholes model - Wikipedia
Black–Scholes model - Wikipedia Black–Scholes model From Wikipedia, the free encyclopedia (Redirected from Black–Scholes) Jump to: navigation, search The Black–Scholes /ˌblæk ˈʃoʊlz/ [1] or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price regardless of the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate). The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. [2]







Flashcard 1736018889996

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#stochastics
Question
a homogeneous Poisson process is defined with a [...]
Answer
single positive constant

The constant denotes a fixed area (or length) on the domain.


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If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process.

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Stochastic process - Wikipedia
arameter. This process has the natural numbers as its state space and the non-negative numbers as its index set. This process is also called the Poisson counting process, since it can be interpreted as an example of a counting process. [99] <span>If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process. [99] [101] The homogeneous Poisson process (in continuous time) is a member of important classes of stochastic processes such as Markov processes and Lévy processes. [49] The homogen







Flashcard 1737981037836

[unknown IMAGE 1737981562124]
Tags
#bayesian-ml #has-images #prml
Question
The joint distribution for the state space model is
Answer
Think about how this plays out in HMM and LDS models.


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Flashcard 1738568240396

Tags
#measure-theory #stochastics
Question
the Cantor set C∞ is a set of Lebesgue measure [...]
Answer
Lebesgue measure zero


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bution attributes probability zero to each of the intervals removed, and the lengths of these intervals add up to one. So all of the probability is concentrated on the Cantor set C ∞ , which is what the measure-theoretic jargon calls a set of <span>Lebesgue measure zero, Lebesgue measure being the measure-theoretic analog of ordinary length. <span><body><html>

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Flashcard 1739078634764

Tags
#forward-backward-algorithm #hmm
Question
The forward–backward algorithm computes the posterior marginals of all hidden state variables given [...]
Answer
a sequence of observations


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The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations

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Forward–backward algorithm - Wikipedia
ackward algorithm - Wikipedia Forward–backward algorithm From Wikipedia, the free encyclopedia (Redirected from Forward-backward algorithm) Jump to: navigation, search <span>The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions o 1 : t := o 1







Flashcard 1756498627852

[unknown IMAGE 1756479753484]
Tags
#has-images #lagrange-multiplier #optimization
Question
at any point on the constraint surface the gradient ∇g(x) of the constraint function will be [...]
Answer
orthogonal to the surface

Otherwise we'd be able to move along g(x) to move away from g(x), which is itself contradictary.
This can be proved using the Taylor expansion of g(x) at any point


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at any point on the constraint surface the gradient ∇g(x) of the constraint function will be orthogonal to the surface

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Flashcard 1758007004428

Tags
#eigen-analysis #spectral-theorem
Question
when applied to it, an eigenvector of a linear transformation only [...]
Answer
changes by a scalar factor


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In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that only changes by a scalar factor, when that linear transformation is applied to it.

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Eigenvalues and eigenvectors - Wikipedia
m Wikipedia, the free encyclopedia (Redirected from Eigenvalue) Jump to: navigation, search "Characteristic root" redirects here. For other uses, see Characteristic root (disambiguation). <span>In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that only changes by a scalar factor, when that linear transformation is applied to it. More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an eigenvector of T if T(v)







Flashcard 1758295887116

Tags
#calculus-of-variations
Question
If a continuous function on an open interval satisfies [...] for all compactly supported smooth functions on , then is identically zero.
Answer
the equality

Using linear algebra analogy, is orthogonal to all s in the vector space, and thus orthogonal to al the bases of the space: it must be the zero vector.


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If a continuous function on an open interval satisfies the equality for all compactly supported smooth functions on , then is identically zero.

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Fundamental lemma of calculus of variations - Wikipedia
[hide] 1 Basic version 2 Version for two given functions 3 Versions for discontinuous functions 4 Higher derivatives 5 Vector-valued functions 6 Multivariable functions 7 Applications 8 Notes 9 References Basic version[edit source] <span>If a continuous function f {\displaystyle f} on an open interval ( a , b ) {\displaystyle (a,b)} satisfies the equality ∫ a b f ( x ) h ( x ) d ⁡ x = 0 {\displaystyle \int _{a}^{b}f(x)h(x)\,\operatorname {d} x=0} for all compactly supported smooth functions h {\displaystyle h} on ( a , b ) {\displaystyle (a,b)} , then f {\displaystyle f} is identically zero. [1] [2] Here "smooth" may be interpreted as "infinitely differentiable", [1] but often is interpreted as "twice continuously differentiable" or "co







Flashcard 1759708843276

Tags
#hilbert-space
Question
This inner product in the space ℂ2 is [...property...]
Answer
Hermitian symmetric


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This inner product in the space ℂ 2 is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate:

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Hilbert space - Wikipedia
2 . {\displaystyle \langle z,w\rangle =z_{1}{\overline {w}}_{1}+z_{2}{\overline {w}}_{2}\,.} The real part of ⟨z,w⟩ is then the four-dimensional Euclidean dot product. <span>This inner product is Hermitian symmetric, which means that the result of interchanging z and w is the complex conjugate: ⟨ w , z ⟩ = ⟨ z , w







Flashcard 1760047795468

Question

[...] solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation.

Answer
separation of variables


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separation of variables solves ordinary and partial differential equations by allowing one to rewrite an equation so that each of two variables occurs on a different side of the equation. </spa

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Separation of variables - Wikipedia
People [show] Isaac Newton Leonhard Euler Émile Picard Józef Maria Hoene-Wroński Ernst Lindelöf Rudolf Lipschitz Augustin-Louis Cauchy John Crank Phyllis Nicolson Carl David Tolmé Runge Martin Wilhelm Kutta v t e <span>In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Contents [hide] 1 Ordinary differential equations (ODE) 1.1 Alternative notation 1.2 Example 2 Partial differential equations 2.1 Example: homogeneous case 2.2 Example:







The nabla is a triangular symbol like an inverted Greek delta: or ∇.

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Nabla symbol - Wikipedia
a Jump to: navigation, search This article is about the nabla symbol, its name, their usage, and their historical origin. See Del for an article focused on the mathematics. ∇ The nabla symbol <span>The nabla is a triangular symbol like an inverted Greek delta: [1] ∇ {\displaystyle \nabla } or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, [2] and was suggested by the encyclopedist William Robertson Smith to Pete




Flashcard 1760775245068

Question
The [...] is a triangular symbol like an inverted Greek delta: or ∇.
Answer
nabla


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The nabla is a triangular symbol like an inverted Greek delta: or ∇.

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Nabla symbol - Wikipedia
a Jump to: navigation, search This article is about the nabla symbol, its name, their usage, and their historical origin. See Del for an article focused on the mathematics. ∇ The nabla symbol <span>The nabla is a triangular symbol like an inverted Greek delta: [1] ∇ {\displaystyle \nabla } or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic Greek word νάβλα for a Phoenician harp, [2] and was suggested by the encyclopedist William Robertson Smith to Pete







#inner-product-space

After defining an inner product on the set of random variables using the expectation of their product,

⟨ X , Y ⟩ := E ⁡ ( X Y ) , {\displaystyle \langle X,Y\rangle :=\operatorname {E} (XY),}

then the Cauchy–Schwarz inequality becomes

| E ⁡ ( X Y ) | 2 ≤ E ⁡ ( X 2 ) E ⁡ ( Y 2 ) . {\displaystyle |\operatorname {E} (XY)|^{2}\leq \operatorname {E} (X^{2})\operatorname {E} (Y^{2}).}

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Cauchy–Schwarz inequality - Wikipedia
( X ) . {\displaystyle \operatorname {Var} (Y)\geq {\frac {\operatorname {Cov} (Y,X)\operatorname {Cov} (Y,X)}{\operatorname {Var} (X)}}.} <span>After defining an inner product on the set of random variables using the expectation of their product, ⟨ X , Y ⟩ := E ⁡ ( X Y ) , {\displaystyle \langle X,Y\rangle :=\operatorname {E} (XY),} then the Cauchy–Schwarz inequality becomes | E ⁡ ( X Y ) | 2 ≤ E ⁡ ( X 2 ) E ⁡ ( Y 2 ) . {\displaystyle |\operatorname {E} (XY)|^{2}\leq \operatorname {E} (X^{2})\operatorname {E} (Y^{2}).} To prove the covariance inequality using the Cauchy–Schwarz inequality, let μ = E ⁡ ( X ) {




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Hilbert curve - Wikipedia
Hilbert curve From Wikipedia, the free encyclopedia Jump to: navigation, search [imagelink] First eight iterations of the Hilbert curve View first 10 iterations <span>A Hilbert curve (also known as a Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, [1] as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. [2] Because it is space-fi




Flashcard 1760805129484

Question
A Hilbert curve is a [...]


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A Hilbert curve is a continuous fractal space-filling curve

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Hilbert curve - Wikipedia
Hilbert curve From Wikipedia, the free encyclopedia Jump to: navigation, search [imagelink] First eight iterations of the Hilbert curve View first 10 iterations <span>A Hilbert curve (also known as a Hilbert space-filling curve) is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891, [1] as a variant of the space-filling Peano curves discovered by Giuseppe Peano in 1890. [2] Because it is space-fi







Analysis of variance (ANOVA) is a collection of statistical models and their associated procedures (such as "variation" among and between groups) used to analyze the differences among group means. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVAs are useful for comparing (testing) three or more means (groups or variables) for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative (results in less type I error) [1] and is therefore suited to a wide range of practical problems.

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Analysis of variance - Wikipedia
/head>Analysis of variance - Wikipedia Analysis of variance From Wikipedia, the free encyclopedia (Redirected from Anova) Jump to: navigation, search Analysis of variance (ANOVA) is a collection of statistical models and their associated procedures (such as "variation" among and between groups) used to analyze the differences among group means. ANOVA was developed by statistician and evolutionary biologist Ronald Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to more than two groups. ANOVAs are useful for comparing (testing) three or more means (groups or variables) for statistical significance. It is conceptually similar to multiple two-sample t-tests, but is more conservative (results in less type I error) [1] and is therefore suited to a wide range of practical problems. Contents [hide] 1 History 2 Motivating example 3 Background and terminology 3.1 Design-of-experiments terms 4 Classes of models 4.1 Fixed-effects models 4.2 Random-effe




#calculus
In calculus, foundations refers to the rigorous development of the subject from axioms and definitions.

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Calculus - Wikipedia
uing development of calculus. One of the first and most complete works on both infinitesimal and integral calculus was written in 1748 by Maria Gaetana Agnesi. [17] [18] [imagelink] Maria Gaetana Agnesi Foundations[edit source] <span>In calculus, foundations refers to the rigorous development of the subject from axioms and definitions. In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley. Berkeley




#calculus
Henri Lebesgue invented measure theory and used it to define integrals of all but the most pathological functions.

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Calculus - Wikipedia
the complex plane. In modern mathematics, the foundations of calculus are included in the field of real analysis, which contains full definitions and proofs of the theorems of calculus. The reach of calculus has also been greatly extended. <span>Henri Lebesgue invented measure theory and used it to define integrals of all but the most pathological functions. Laurent Schwartz introduced distributions, which can be used to take the derivative of any function whatsoever. Limits are not the only rigorous approach to the foundation of calculus




#calculus
Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities

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Calculus - Wikipedia
otype of an (ε, δ)-definition of limit in the definition of differentiation. [20] In his work Weierstrass formalized the concept of limit and eliminated infinitesimals (although his definition can actually validate nilsquare infinitesimals). <span>Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus". Bernhard Riemann used these ideas to give a precise definition of the integral. It was also during t




[unknown IMAGE 1760828984588]
#calculus #has-images

The (ε, δ)-definition of limit defines the limit of a function f at point c as: whenever a point x is within δ units of c, f(x) is within ε units of L

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(ε, δ)-definition of limit - Wikipedia
ion of limit - Wikipedia (ε, δ)-definition of limit From Wikipedia, the free encyclopedia (Redirected from Epsilon, delta) Jump to: navigation, search [imagelink] <span>Whenever a point x is within δ units of c, f(x) is within ε units of L In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy,




Flashcard 1760832130316

[unknown IMAGE 1760828984588]
Tags
#calculus #has-images
Question

The (ε, δ)-definition of limit defines the limit of a function f at point c as: [...]

Answer
whenever a point x is within δ units of c, f(x) is within ε units of L


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The (ε, δ)-definition of limit defines the limit of a function f at point c as: whenever a point x is within δ units of c, f(x) is within ε units of L

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(ε, δ)-definition of limit - Wikipedia
ion of limit - Wikipedia (ε, δ)-definition of limit From Wikipedia, the free encyclopedia (Redirected from Epsilon, delta) Jump to: navigation, search [imagelink] <span>Whenever a point x is within δ units of c, f(x) is within ε units of L In calculus, the (ε, δ)-definition of limit ("epsilon–delta definition of limit") is a formalization of the notion of limit. The concept is due to Augustin-Louis Cauchy,







#calculus

The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals.

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Calculus - Wikipedia
infinitesimals. The symbols dx and dy were taken to be infinitesimal, and the derivative d y / d x {\displaystyle dy/dx} was simply their ratio. <span>The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a near




#calculus
In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits were the first way to provide rigorous foundations for calculus, and for this reason they are the standard approach.

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Calculus - Wikipedia
ion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. <span>In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits were the first way to provide rigorous foundations for calculus, and for this reason they are the standard approach. Differential calculus[edit source] Main article: Differential calculus [imagelink] Tangent line at (x, f(x)). The derivative f′(x) of a curve at a point is the slope (rise ov




#calculus
In formal terms, the derivative is a linear operator which takes a function as its input and produces a second function as its output.

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Calculus - Wikipedia
ll-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the derivative function or just the derivative of the original function. <span>In formal terms, the derivative is a linear operator which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling function i




#calculus
The most common symbol for a derivative is an apostrophe-like mark called prime.

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Calculus - Wikipedia
2 ", as an input, that is all the information —such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on— and uses this information to output another function, the function g(x) = 2x, as will turn out. <span>The most common symbol for a derivative is an apostrophe-like mark called prime. Thus, the derivative of a function called f is denoted by f′, pronounced "f prime". For instance, if f(x) = x 2 is the squaring function, then f′(x) = 2x is its derivative (t




#calculus

The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero:

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Calculus - Wikipedia
e behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is undefined. <span>The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero: lim h → 0 f ( a + h ) − f ( a ) h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference




#calculus
The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients.

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Calculus - Wikipedia
h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. <span>The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. For this reason, the derivative is sometimes called the slope of the function f. Here is a particular example, the derivative of the squaring function at the input 3. Let f(x) = x 2




#calculus
In an approach based on limits, the symbol dy / dx is to be interpreted not as the quotient of two numbers but as a shorthand for the limit

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Calculus - Wikipedia
= 2 x . {\displaystyle {\begin{aligned}y&=x^{2}\\{\frac {dy}{dx}}&=2x.\end{aligned}}} <span>In an approach based on limits, the symbol dy/dx is to be interpreted not as the quotient of two numbers but as a shorthand for the limit computed above. Leibniz, however, did intend it to represent the quotient of two infinitesimally small numbers, dy being the infinitesimally small change in y caused by an infinitesimal




#calculus
Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were real numbers

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Calculus - Wikipedia
2 ) = 2 x . {\displaystyle {\frac {d}{dx}}(x^{2})=2x.} In this usage, the dx in the denominator is read as "with respect to x". <span>Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were real numbers; although it is possible to avoid such manipulations, they are sometimes notationally convenient in expressing operations such as the total derivative. Integral calculus[edit source]




#calculus
Calculation of the total derivative of with respect to assumes that the other arguments too depend on t.

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Total derivative - Wikipedia
effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). <span>Calculation of the total derivative of f {\displaystyle f} with respect to t {\displaystyle t} does not assume that the other arguments are constant while t {\displaystyle t} varies; instead, it assumes that the other arguments too depend on t {\displaystyle t} . The total derivative includes these indirect dependencies to find the overall dependency of f {\displaystyle f} on t




#calculus
The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

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Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the




Flashcard 1760858606860

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#calculus
Question
The total derivative is the [...description...]
Answer
limiting ratio of ∆ƒ/∆t


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The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function.

Original toplevel document

Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the







Flashcard 1760860179724

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#calculus
Question
The total derivative taking into account the exogenous argument's [...] to the function
Answer
direct and indirect effects


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a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value, taking into account the exogenous argument's <span>direct effect as well as indirect effects via the other arguments of the function. <span><body><html>

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Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the







Flashcard 1760861752588

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#calculus
Question
The [...] of a function of several variables, e.g., , , , with respect to an exogenous argument is defined as
Answer
total derivative


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The total derivative of a function of several variables, e.g., , , , with respect to an exogenous argument , is the limiting ratio of the change in the function's value to the change in the exogenous ar

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Total derivative - Wikipedia
integral Line integral Surface integral Volume integral Jacobian Hessian Specialized[show] Fractional Malliavin Stochastic Variations Glossary of calculus[show] Glossary of calculus v t e <span>In the mathematical field of differential calculus, a total derivative or full derivative of a function f {\displaystyle f} of several variables, e.g., t {\displaystyle t} , x {\displaystyle x} , y {\displaystyle y} , etc., with respect to an exogenous argument, e.g., t {\displaystyle t} , is the limiting ratio of the change in the function's value to the change in the exogenous argument's value (for arbitrarily small changes), taking into account the exogenous argument's direct effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). Calculation of the







Flashcard 1760864111884

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#calculus
Question
Calculation of the total derivative of with respect to assumes that [...].
Answer
the other arguments too depend on t


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Calculation of the total derivative of with respect to assumes that the other arguments too depend on t.

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Total derivative - Wikipedia
effect as well as indirect effects via the other arguments of the function. The total derivative of a function is different from its corresponding partial derivative ( ∂ {\displaystyle \partial } ). <span>Calculation of the total derivative of f {\displaystyle f} with respect to t {\displaystyle t} does not assume that the other arguments are constant while t {\displaystyle t} varies; instead, it assumes that the other arguments too depend on t {\displaystyle t} . The total derivative includes these indirect dependencies to find the overall dependency of f {\displaystyle f} on t







Flashcard 1760865684748

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#calculus
Question
In calculus, foundations refers to the rigorous development of the subject from [...] .
Answer
axioms and definitions


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In calculus, foundations refers to the rigorous development of the subject from axioms and definitions.

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Calculus - Wikipedia
uing development of calculus. One of the first and most complete works on both infinitesimal and integral calculus was written in 1748 by Maria Gaetana Agnesi. [17] [18] [imagelink] Maria Gaetana Agnesi Foundations[edit source] <span>In calculus, foundations refers to the rigorous development of the subject from axioms and definitions. In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley. Berkeley







Flashcard 1760868044044

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#calculus
Question
In calculus, [...] refers to the rigorous development of the subject from axioms and definitions.
Answer
foundations


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In calculus, foundations refers to the rigorous development of the subject from axioms and definitions.

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Calculus - Wikipedia
uing development of calculus. One of the first and most complete works on both infinitesimal and integral calculus was written in 1748 by Maria Gaetana Agnesi. [17] [18] [imagelink] Maria Gaetana Agnesi Foundations[edit source] <span>In calculus, foundations refers to the rigorous development of the subject from axioms and definitions. In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley. Berkeley







Flashcard 1760869616908

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#calculus
Question
Following the work of Weierstrass, it eventually became common to base calculus on [...] instead of infinitesimal quantities
Answer
limits


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Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities

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Calculus - Wikipedia
otype of an (ε, δ)-definition of limit in the definition of differentiation. [20] In his work Weierstrass formalized the concept of limit and eliminated infinitesimals (although his definition can actually validate nilsquare infinitesimals). <span>Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus". Bernhard Riemann used these ideas to give a precise definition of the integral. It was also during t







Flashcard 1760871189772

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Henri Lebesgue invented [...] and used it to define integrals of all but the most pathological functions.


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Henri Lebesgue invented measure theory and used it to define integrals of all but the most pathological functions.

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the complex plane. In modern mathematics, the foundations of calculus are included in the field of real analysis, which contains full definitions and proofs of the theorems of calculus. The reach of calculus has also been greatly extended. <span>Henri Lebesgue invented measure theory and used it to define integrals of all but the most pathological functions. Laurent Schwartz introduced distributions, which can be used to take the derivative of any function whatsoever. Limits are not the only rigorous approach to the foundation of calculus







#calculus
The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise.

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The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulat

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Calculus - Wikipedia
infinitesimals. The symbols dx and dy were taken to be infinitesimal, and the derivative d y / d x {\displaystyle dy/dx} was simply their ratio. <span>The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a near




Flashcard 1760874335500

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#calculus
Question
The infinitesimal approach fell out of favor in the [...] century because it was difficult to make the notion of an infinitesimal precise.
Answer
19th


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The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise.

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Calculus - Wikipedia
infinitesimals. The symbols dx and dy were taken to be infinitesimal, and the derivative d y / d x {\displaystyle dy/dx} was simply their ratio. <span>The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a near







Flashcard 1760876170508

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#calculus
Question
The infinitesimal approach fell out of favor in the 19th century because it was difficult to make [...]
Answer
the notion of an infinitesimal precise.


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The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise.

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Calculus - Wikipedia
infinitesimals. The symbols dx and dy were taken to be infinitesimal, and the derivative d y / d x {\displaystyle dy/dx} was simply their ratio. <span>The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a near







Flashcard 1760877743372

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#calculus
Question
In the 19th century, infinitesimals were replaced by [...]
Answer
the epsilon, delta approach to limits.


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In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this

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Calculus - Wikipedia
ion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. <span>In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits were the first way to provide rigorous foundations for calculus, and for this reason they are the standard approach. Differential calculus[edit source] Main article: Differential calculus [imagelink] Tangent line at (x, f(x)). The derivative f′(x) of a curve at a point is the slope (rise ov







Flashcard 1760880102668

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#calculus
Question
Limits describe the value of a function at a certain input in terms of [...].
Answer
its values at nearby inputs


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In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals ge

Original toplevel document

Calculus - Wikipedia
ion of an infinitesimal precise. However, the concept was revived in the 20th century with the introduction of non-standard analysis and smooth infinitesimal analysis, which provided solid foundations for the manipulation of infinitesimals. <span>In the 19th century, infinitesimals were replaced by the epsilon, delta approach to limits. Limits describe the value of a function at a certain input in terms of its values at a nearby input. They capture small-scale behavior in the context of the real number system. In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by very small numbers, and the infinitely small behavior of the function is found by taking the limiting behavior for smaller and smaller numbers. Limits were the first way to provide rigorous foundations for calculus, and for this reason they are the standard approach. Differential calculus[edit source] Main article: Differential calculus [imagelink] Tangent line at (x, f(x)). The derivative f′(x) of a curve at a point is the slope (rise ov







Flashcard 1760882461964

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#calculus
Question
In formal terms, the derivative is a [...] which takes a function as its input and produces a second function as its output.
Answer
linear operator


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In formal terms, the derivative is a linear operator which takes a function as its input and produces a second function as its output.

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ll-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the derivative function or just the derivative of the original function. <span>In formal terms, the derivative is a linear operator which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling function i







Flashcard 1760884034828

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#calculus
Question
The most common symbol for a derivative is an apostrophe-like mark called [...].
Answer
prime


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The most common symbol for a derivative is an apostrophe-like mark called prime.

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Calculus - Wikipedia
2 ", as an input, that is all the information —such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on— and uses this information to output another function, the function g(x) = 2x, as will turn out. <span>The most common symbol for a derivative is an apostrophe-like mark called prime. Thus, the derivative of a function called f is denoted by f′, pronounced "f prime". For instance, if f(x) = x 2 is the squaring function, then f′(x) = 2x is its derivative (t







Flashcard 1760886656268

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#calculus
Question

The derivative is defined as [...formula...]

Answer


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The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero:

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Calculus - Wikipedia
e behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is undefined. <span>The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero: lim h → 0 f ( a + h ) − f ( a ) h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference







#calculus
derivative defined by limit considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero

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The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero:

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Calculus - Wikipedia
e behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is undefined. <span>The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero: lim h → 0 f ( a + h ) − f ( a ) h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference




Flashcard 1760891374860

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#calculus
Question
derivative defined by limit considers [...] and extracts a consistent value for the exact point
Answer
the behavior of f at nearby inputs


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derivative defined by limit considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero

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Calculus - Wikipedia
e behavior of the function at the point a because it does not account for what happens between a and a + h. It is not possible to discover the behavior at a by setting h to zero because this would require dividing by zero, which is undefined. <span>The derivative is defined by taking the limit as h tends to zero, meaning that it considers the behavior of f for all small values of h and extracts a consistent value for the case when h equals zero: lim h → 0 f ( a + h ) − f ( a ) h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. The tangent line is a limit of secant lines just as the derivative is a limit of difference







Flashcard 1760893734156

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#calculus
Question
The tangent line is a limit of [...] just as the derivative is a limit of difference quotients.
Answer
secant lines


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The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients.

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h . {\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.} Geometrically, the derivative is the slope of the tangent line to the graph of f at a. <span>The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. For this reason, the derivative is sometimes called the slope of the function f. Here is a particular example, the derivative of the squaring function at the input 3. Let f(x) = x 2







Flashcard 1760895307020

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Question
In an approach based on limits, the symbol dy / dx is to be interpreted not as the quotient of two numbers but as [...]
Answer
a shorthand for the limit


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In an approach based on limits, the symbol dy / dx is to be interpreted not as the quotient of two numbers but as a shorthand for the limit

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= 2 x . {\displaystyle {\begin{aligned}y&=x^{2}\\{\frac {dy}{dx}}&=2x.\end{aligned}}} <span>In an approach based on limits, the symbol dy/dx is to be interpreted not as the quotient of two numbers but as a shorthand for the limit computed above. Leibniz, however, did intend it to represent the quotient of two infinitesimally small numbers, dy being the infinitesimally small change in y caused by an infinitesimal







Flashcard 1760896879884

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Question
Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were [...]
Answer
real numbers


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Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were real numbers

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2 ) = 2 x . {\displaystyle {\frac {d}{dx}}(x^{2})=2x.} In this usage, the dx in the denominator is read as "with respect to x". <span>Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like dx and dy as if they were real numbers; although it is possible to avoid such manipulations, they are sometimes notationally convenient in expressing operations such as the total derivative. Integral calculus[edit source]







Article 1760904482060

The Absolute Superlative
#spanish

The absolute superlative indicates the highest or lowest quality grade, i.e. it can express superiority or inferiority. The absolute superlative of superiority can be expressed in the following ways: Muy (very) + adjective: Este chico es muy guapo (This guy is very handsome). Esa obra de teatro parece muy interesante (That theatre play looks very interesting). Suffixes -ísimo, -ísima may also be added: Este chico es guapísimo. Esa obra de teatro parece interesantísima. The absolute superlative of inferiority can be expressed in the following ways: (Muy) poco [(very) little] + positive adjective. It is used to express politely that you dislike something. Es muy poco agradable (He/She is not very kind). El documental es poco interesante (The documentary is not very interesting). Suffixes -ísimo, -ísima with negative adjectives. Esa obra de teatro es aburridísima (That theatre play is very boring). Ese cuadro es feísimo (That painting



#spanish
Es muy poco agradable (He/She is not very kind).

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The Absolute Superlative
3; The absolute superlative of inferiority can be expressed in the following ways: (Muy) poco [(very) little] + positive adjective. It is used to express politely that you dislike something. <span>Es muy poco agradable (He/She is not very kind). El documental es poco interesante (The documentary is not very interesting). Suffixes -ísimo, -ísima with negative adjectives. Esa obra de teatro es aburri




Flashcard 1760908938508

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#spanish
Question
Es [...] agradable (He/She is not very kind).
Answer
muy poco


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Es muy poco agradable (He/She is not very kind).

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The Absolute Superlative
3; The absolute superlative of inferiority can be expressed in the following ways: (Muy) poco [(very) little] + positive adjective. It is used to express politely that you dislike something. <span>Es muy poco agradable (He/She is not very kind). El documental es poco interesante (The documentary is not very interesting). Suffixes -ísimo, -ísima with negative adjectives. Esa obra de teatro es aburri







Article 1760910511372

Verb Phrases (I) - Infinitive
#spanish

A verb periphrasis is the combination of two verb forms, one conjugated and the other one a non-finite form (infinitive, gerund, past participle). Sometimes there is a conjunction or preposition that links those verbs. The most important verb phrases with infinitive are the following: Periphrasis Meaning Example haber que(impersonal use, 3rd person: hayque) + infinitive obligation, advice Hay que ir a la compra: no tenemos nada en lanevera (We have to do the shopping. There is nothing in our fridge). deber + infinitive obligation, advice Estás demasiado delgado: debes comer más(You are too thin. You should eat more). tener que + infinitive obligation, advice Tienes que estudiar mucho hoy porquemañana tienes el examen final (You must study a lot today because your final exam is taking place tomorrow). poder + infinitive possibility, permission No puedes comer aquí (You cannot eat in here). volver a + infinitive reiteration Vuelve a decirle que me llame (Tell her to call me again). empezar a



#spanish
Vuelve a decirle que me llame (Tell her to call me again).

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Verb Phrases (I) - Infinitive
hoy porquemañana tienes el examen final (You must study a lot today because your final exam is taking place tomorrow). poder + infinitive possibility, permission No puedes comer aquí (You cannot eat in here). volver a + infinitive reiteration <span>Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis a




#spanish
Empezamos a correr cuando vimos que llovía

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Verb Phrases (I) - Infinitive
xam is taking place tomorrow). poder + infinitive possibility, permission No puedes comer aquí (You cannot eat in here). volver a + infinitive reiteration Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start <span>Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit Suelo comer en una tasc




#spanish
Luis y Ana acaban de irse (Luis and Ana have just left).

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Verb Phrases (I) - Infinitive
lver a + infinitive reiteration Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy <span>Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work). ir a + infinitive near future Voy a comer a casa de mis tíos (I am goi




#spanish
Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work).

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Verb Phrases (I) - Infinitive
again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit <span>Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work). ir a + infinitive near future Voy a comer a casa de mis tíos (I am going to eat at my uncle and aunt’s). <span><body><html>




Flashcard 1760918375692

Tags
#spanish
Question
[...] decirle que me llame (Tell her to call me again).
Answer
Vuelve a


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Vuelve a decirle que me llame (Tell her to call me again).

Original toplevel document

Verb Phrases (I) - Infinitive
hoy porquemañana tienes el examen final (You must study a lot today because your final exam is taking place tomorrow). poder + infinitive possibility, permission No puedes comer aquí (You cannot eat in here). volver a + infinitive reiteration <span>Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis a







Flashcard 1760919948556

Tags
#spanish
Question
[...] correr cuando vimos que llovía
Answer
Empezamos a


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Empezamos a correr cuando vimos que llovía

Original toplevel document

Verb Phrases (I) - Infinitive
xam is taking place tomorrow). poder + infinitive possibility, permission No puedes comer aquí (You cannot eat in here). volver a + infinitive reiteration Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start <span>Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit Suelo comer en una tasc







Flashcard 1760921521420

Tags
#spanish
Question
Luis y Ana [...] irse (Luis and Ana have just left).
Answer
acaban de


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Luis y Ana acaban de irse (Luis and Ana have just left).

Original toplevel document

Verb Phrases (I) - Infinitive
lver a + infinitive reiteration Vuelve a decirle que me llame (Tell her to call me again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy <span>Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work). ir a + infinitive near future Voy a comer a casa de mis tíos (I am goi







Flashcard 1760923094284

Tags
#spanish
Question
[...] comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work).
Answer
Suelo


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Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work).

Original toplevel document

Verb Phrases (I) - Infinitive
again). empezar a + infinitive start Empezamos a correr cuando vimos que llovía(We started to run when we saw it was raining). acabar de + infinitive immediacy Luis y Ana acaban de irse (Luis and Ana have just left). soler + infinitive habit <span>Suelo comer en una tasca cerca del trabajo (I usually have lunch at a bar close to work). ir a + infinitive near future Voy a comer a casa de mis tíos (I am going to eat at my uncle and aunt’s). <span><body><html>







Bioenergetics concerns only the initial and final energy states of reaction components, not the mechanism or how much time is needed for the chemical change to take place. In short, bio - energetics predicts if a process is possible, whereas kinetics measures how fast the reaction occurs.

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The direction and extent to which a chemical reaction proceeds is determined by the degree to which two factors change during the reaction. These are enthalpy (ΔH, a measure of the change in heat con- tent of the reactants and products) and entropy (ΔS, a measure of the change in randomness or disorder of reactants and products, Figure 6.1). Neither of these thermodynamic quantities by itself is sufficient to determine whether a chemical reaction will proceed spontaneously in the direction it is written. However, when combined mathematically (see Figure 6.1), enthalpy and entropy can be used to define a third quantity, free energy (G), which predicts the direction in which a reaction will spontaneously proceed.

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1. Negative ΔG: If ΔG is a negative number, there is a net loss of energy, and the reaction goes spontaneously as written—that is, A is converted into B (Figure 6.2A). The reaction is said to be exergonic. 2. Positive ΔG: If ΔG is a positive number, there is a net gain of energy, and the reaction does not go spontaneously from B to A (see Figure 6.2B). Energy must be added to the system to make the reaction go from B to A, and the reaction is said to be ender- gonic. 3. ΔG is zero: If ΔG = 0, the reactants are in equilibrium. [Note: When a reaction is proceeding spontaneously—that is, free energy is being lost—then the reaction continues until ΔG reaches zero and equilibrium is established.]

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B. ΔG of the forward and back reactions The free energy of the forward reaction (A → B) is equal in magni- tude but opposite in sign to that of the back reaction (B → A). For example, if ΔG of the forward reaction is −5 kcal/mol, then that of the back reaction is +5 kcal/mol. [Note: ΔG can also be expressed in kilo- joules per mole or kJ/mol (1 kcal = 4.2 kJ).] C. ΔG depends on the concentration of reactants and products The ΔG of the reaction A → B depends on the concentration of the reactant and product. At constant temperature and pressure, the fol- lowing relationship can be derived: ΔG = ∆Go equation. Edit this.

A reaction with a positive ΔGo
can proceed in the forward direction
(have a negative overall ΔG) if the ratio of products to reactants
([B]/[A] ) is sufficiently small (that is, the ratio of reactants to products
is large).

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2. Relationship between ΔG o and K eq : In a reaction A → B, a point of equilibrium is reached at which no further net chemical change takes place—that is, when A is being converted to B as fast as B is being converted to A. In this state, the ratio of [B] to [A] is con- stant, regardless of the actual concentrations of the two compounds:

Keq = [B]eq/[A]eq

where K eq is the equilibrium constant, and [A] eq and [B] eq are the concentrations of A and B at equilibrium. If the reaction A B is allowed to go to equilibrium at constant temperature and pres- sure, then at equilibrium the overall free energy change (ΔG) is zero. Therefore, where the actual concentrations of A and B are equal to the equi- librium concentrations of reactant and product [A] eq and [B] eq , and their ratio as shown above is equal to the K eq. Thus,

∆G = ∆Go - RTlnKeq

This equation allows for some simple predictions:

If Keq = 1, then ∆Go = 0 and A <--> B
If Keq > 1, then ∆Go < 0 and A <---->>>> B
If Keq < 1, then ∆Go > 0 and A <<<<------> B

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ΔGs of a pathway are additive: This additive property of free energy changes is very important in biochemical pathways through which substrates must pass in a particular direction (for example, A → B → C → D → ...). As long as the sum of the ΔGs of the individual reactions is negative, the pathway can potentially proceed as written, even if some of the individual reactions of the pathway have a positive ΔG. The actual rate of the reactions does, of course, depend on the lowering of activation energies by the enzymes that catalyze the reactions.

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Energy-rich molecules, such as glucose, are metabolized by a series of oxidation reactions ultimately yielding CO2 and water (Figure 6.6). The metabolic intermediates of these reactions donate electrons to specific coenzymes—nicotinamide adenine dinucleotide (NAD + ) and flavin adenine dinucleotide (FAD)—to form the energy-rich reduced coen- zymes, NADH and FADH 2 . These reduced coenzymes can, in turn, each donate a pair of electrons to a specialized set of electron carriers, collectively called the electron transport chain, described in this section. As electrons are passed down the electron transport chain, they lose much of their free energy. Part of this energy can be captured and stored by the production of ATP from ADP and inorganic phosphate (Pi). This process is called oxidative phosphorylation and is described on p. 77. The remainder of the free energy not trapped as ATP is used to drive ancillary reactions such as Ca 2+ transport into mitochondria, and to generate heat

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Matrix of the mitochondrion: This gel-like solution in the interior of mitochondria is 50% protein. These molecules include the enzymes responsible for the oxidation of pyruvate, amino acids, fatty acids (by β-oxidation), and those of the tricarboxylic acid (TCA) cycle. The synthesis of glucose, urea, and heme occur partially in the matrix of mitochondria. In addition, the matrix contains NAD + and FAD (the oxidized forms of the two coenzymes that are required as hydrogen acceptors) and ADP and P i , which are used to produce ATP. [Note: The matrix also contains mitochondrial RNA and DNA (mtRNA and mtDNA) and mitochondrial ribosomes.]

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The inner mitochondrial membrane can be disrupted into five sepa- rate protein complexes, called Complexes I, II, III, IV, and V. Complexes I–IV each contain part of the electron transport chain (Figure 6.8). Each complex accepts or donates electrons to relatively mobile electron carriers, such as coenzyme Q and cytochrome c. Each carrier in the electron transport chain can receive electrons from an electron donor, and can subsequently donate electrons to the next carrier in the chain. The electrons ultimately combine with oxygen and protons to form water. This requirement for oxygen makes the electron transport process the respiratory chain , which accounts for the greatest portion of the body’s use of oxygen.

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With the exception of coenzyme Q, all members of this chain are proteins

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Formation of NADH: NAD + is reduced to NADH by dehydroge- nases that remove two hydrogen atoms from their substrate. (For examples of these reactions, see the discussion of the dehydro- genases found in the TCA cycle, p. 112.) Both electrons but only one proton (that is, a hydride ion, :H – ) are transferred to the NAD + , forming NADH plus a free proton, H +

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NADH dehydrogenase: The free proton plus the hydride ion car- ried by NADH are next transferred to NADH dehydrogenase , a protein complex (Complex I) embedded in the inner mitochondrial membrane. Complex I has a tightly bound molecule of flavin mono nucleotide (FMN, a coenzyme structurally related to FAD, see Figure 28.15, p. 380) that accepts the two hydrogen atoms (2e – + 2H + ), becoming FMNH 2 . NADH dehydrogenase also con- tains iron atoms paired with sulfur atoms to make iron–sulfur cen- ters (Figure 6.9). These are necessary for the transfer of the hydrogen atoms to the next member of the chain, coenzyme Q (ubiquinone)

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Coenzyme Q: Coenzyme Q (CoQ) is a quinone derivative with a long, hydrophobic isoprenoid tail. It is also called ubiquinone because it is ubiquitous in biologic systems. CoQ is a mobile car- rier and can accept hydrogen atoms both from FMNH 2 , produced on NADH dehydrogenase (Complex I), and from FADH 2 , pro- duced on succinate dehydrogenase (Complex II), glycerophos- phate dehydrogenase (see p. 79), and acyl CoA dehydrogenase (see p. 192). CoQ transfers electrons to Complex III. CoQ, then, links the flavoproteins to the cytochromes

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Cytochromes: The remaining members of the electron transport chain are cytochromes. Each contains a heme group (a porphyrin ring plus iron). Unlike the heme groups of hemoglobin, the cytochrome iron is reversibly converted from its ferric (Fe 3+ ) to its ferrous (Fe 2+ ) form as a normal part of its function as a reversible carrier of electrons. Electrons are passed along the chain from CoQ to cytochromes

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Cytochrome a + a 3 : This cytochrome complex is the only electron carrier in which the heme iron has an available coordination site that can react directly with O 2 , and so also is called cytochrome oxidase . At this site, the transported electrons, O 2 , and free pro- tons are brought together, and O 2 is reduced to water

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Free energy is released as electrons are transferred along the elec- tron transport chain from an electron donor (reducing agent or reductant) to an electron acceptor (oxidizing agent or oxidant). The electrons can be transferred as hydride ions (:H – ) to NAD + , as hydrogen atoms ( • H) to FMN, coenzyme Q, and FAD, or as elec- trons (e – ) to cytochromes.

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Standard reduction potential (E o ): The E o of various redox pairs can be ordered from the most negative E o to the most positive. The more negative the E o of a redox pair, the greater the tendency of the reductant member of that pair to lose electrons. The more posi- tive the E o , the greater the tendency of the oxidant member of that pair to accept electrons. Therefore, electrons flow from the pair with the more negative E o to that with the more positive E o . The E o values for some members of the electron transport chain are shown in Figure 6.12. [Note: The components of the electron trans- port chain are arranged in order of increasingly positive E 0 values.]

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ΔGo is related to ΔEο: The change in free energy is related directly to the magnitude of the change in Eo:
ΔGo = – nFΔEo
n = number of electrons transferred (1 for a cyto chrome, 2 for NADH, FADH 2 , and coenzyme Q)
F = Faraday constant (23.1 kcal/volt • mol)
ΔEo = Eo of the electron-accepting pair minus the Eo of the electron-donating pair
ΔGo = change in the standard free energy

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The transfer of electrons down the electron transport chain is energeti- cally favored because NADH is a strong electron donor and molecular oxygen is an avid electron acceptor.

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The chemiosmotic hypothesis (also known as the Mitchell hypothesis) explains how the free energy generated by the transport of electrons by the electron transport chain is used to produce ATP from ADP + P i

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Uncoupling proteins (UCP): UCPs occur in the inner mito- chondrial membrane of mammals, including humans. These car- rier proteins create a “proton leak,” that is, they allow protons to re-enter the mitochondrial matrix without energy being captured as ATP (Figure 6.14). The energy is released as heat, and the process is called nonshivering thermogenesis

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Synthetic uncouplers: Electron transport and phosphoryla- tion can also be uncoupled by compounds that increase the permeability of the inner mitochondrial membrane to protons. The classic example is 2,4-dinitrophenol, a lipophilic proton carrier that readily diffuses through the mitochondrial mem- brane. This uncoupler causes electron transport to proceed at a rapid rate without establishing a proton gradient, much as do the UCPs (see Figure 6.14). Again, energy is released as heat rather than being used to synthesize ATP. In high doses, aspirin and other salicylates uncouple oxidative phos - phorylation. This explains the fever that accompanies toxic overdoses of these drugs

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The inner mitochondrial membrane is impermeable to most charged or hydrophilic substances. However, it contains numerous transport proteins that permit passage of specific molecules from the cytosol (or more correctly, the intermembrane space) to the mitochondrial matrix.

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ATP-ADP transport: The inner mitochondrial membrane requires specialized carriers to transport ADP and P i from the cytosol (where ATP is used and converted to ADP in many energy- requiring reactions) into mitochondria, where ATP can be resyn- thesized. An adenine nucleotide carrier imports one molecule of ADP from the cytosol into mitochondria, while exporting one ATP from the matrix back into the cytosol

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Transport of reducing equivalents: The inner mitochondrial mem- brane lacks an NADH transporter, and NADH produced in the cytosol cannot directly enter the mitochondrial matrix. However, two electrons of NADH (also called reducing equivalents) are transported from the cytosol into the matrix using substrate shut- tles. In the glycero phosphate shuttle (Figure 6.15A), two electrons are transferred from NADH to dihydroxyacetone phosphate by cytosolic glycero phosphate dehydrogenase . The glycerol 3-phos- phate produced is oxidized by the mitochondrial isozyme as FAD is reduced to FADH 2 . CoQ of the electron transport chain oxidizes FADH 2 . The glycero phos phate shuttle, therefore, results in the syn- thesis of two ATPs for each cytosolic NADH oxidized. This con- trasts with the malate-aspartate shuttle (Figure 6.15B), which produces NADH (rather than FADH 2 ) in the mitochondrial matrix and, therefore, yields three ATPs for each cytosolic NADH oxidized by malate dehydrogenase as oxaloacetate is reduced to malate. A transport protein carries malate into the matrix.

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Inherited defects in oxidative phosphorylation Thirteen of the approximately 120 polypeptides required for oxida- tive phosphorylation are coded for by mtDNA and synthesized in mitochondria, whereas the remaining mitochondrial proteins are synthesized in the cytosol and transported into mitochondria. Defects in oxidative phosphorylation are more likely a result of alter- ations in mtDNA, which has a mutation rate about ten times greater than that of nuclear DNA. Tissues with the greatest ATP requirement (for example, central nervous system, skeletal and heart muscle, kidney, and liver) are most affected by defects in oxidative phospho- rylation. Mutations in mtDNA are responsible for several diseases, including some cases of mitochondrial myopathies (Figure 6.16), and Leber hereditary optic neuropathy, a disease in which bilateral loss of central vision occurs as a result of neuroretinal degeneration, including damage to the optic nerve. The mtDNA is maternally inher- ited because mitochondria from the sperm cell do not enter the fertil- ized egg.

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Explain why and how the malate-aspartate shuttle moves NADH reducing equivalents from the cytosol to the mitochondrial matrix.

There is no transporter for NADH in the inner mitochondrial membrane. However, NADH can be oxidized to NAD + by the cytoplasmic isozyme of malate dehydrogenase as oxaloac- etate is reduced to malate. The malate is transported across the inner membrane, and the mitochondrial isozyme of malate dehydro- genase oxidizes it to oxaloacetate as mito- chondrial NAD + is reduced to NADH. This NADH can be oxidized by Complex I of the electron transport chain, generating three ATP through the coupled processes of respiration and oxidative phosphorylation.

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Repair the common areas, where all tenants move around freely. This includes hallways, basements, pool area, clubhouse, and so on. Get those areas looking good, even if it costs you.

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Audit your rent roll. Determine which leases will expire within the next 30 to 60 days. Have your manager visit these tenants,

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When repairs are complete, your manager visits all tenants again and offers them a bonus to sign a new lease for another year, at the higher market rate.

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keep tenant turnover at a mini- mum while you significantly increase rents.

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The great opportunity to increase the value of your property quickly is to find properties with low rents.

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researchers did exit polling to discover the main reasons why tenants moved out. Rising rental rates was number three on the list. Number one was failure to take care of repair requests.

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When is it time to raise rents? Any time your property is at 95 per- cent occupancy or above.

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ou should also raise your rents every year, even if the market has not gone up. Train your tenants to expect some annual rent increase. Perhaps it’s only $15 to $20. This is called a nuisance increase.

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You have a 10-unit building, and you increase rents by $20 per month.

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At a 10 Cap Rate, we divide the $2,400 by .10 to arrive at a property value increase of $24,000.

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The faster you go big, the faster you become wealthy.

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if you have a 100-unit apartment building and do a nuisance increase of $20 per month, your cash flow just increased by: 100 units times $20 per month = $2,000 . . . times 12 months = $24,000 per year!

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$240,000 value increase divided by .2 = $1,200,000 more property you can own! All due to a nuisance increase.

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if you raise a C– property to a B–, very few tenants can afford the higher rent you should be charging.

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I bought the property for $58,000. Before I closed, I worked out an arrangement with the local and state police departments to stake out the property. I agreed to give them access to the property whenever they wanted. In return, they would help get rid of the drug dealers.

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take this 365-unit property from a C− toaC+or even B−. The process is what you just read earlier: Do the exterior and common area repairs, and get rid of the slow-payers, non-payers, and criminals.

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have the interior of all units upgraded from their current condi- tion to a grade higher. This includes all new paint, carpet, appliances, cabinet faces, counters, and lighting.

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soak up the concepts, which apply to both the 6-unit and the 365-unit deals.

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you have your market- ing game going, a lot of properties will be coming to you in a short period. You must have a quick and efficient way to determine whether you should take the next step and make an offer on a property.

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you’ve become special only when brokers call you before deals hit the list. Until you get to that point, you must be hyper-responsive.

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By being very responsive to brokers, you will start working your way up their preferred buyers list.

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Very few investors respond by phone to those e-mails. A few respond by e-mail, but the vast majority don’t respond at all. You are going to stand out from the crowd because you’ll call these brokers. You’ll thank them for sending you the deal, even though you know you’re just on the mass mailing list. Then you’ll explain why the deal does or does not work.

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Explain why it doesn’t work, and then explain how you do like to buy (unit size, cap rate, and so on). Then ask: Do you have any deals that fit those criteria? Depending on how far up you are on his list, how much rapport you’ve built, you might get an: Actually, I do have this one deal on the south side of town. . . . Then again, it may take more cultivating.

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train your brokers that you are a professional investor,

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In the commercial real estate world, the value of a property is determined by its cash flow and cap rate.

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