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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.
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
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 [...]
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

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#bayesian-ml #has-images #prml
[unknown IMAGE 1737981562124]
Question
The joint distribution for the state space model is
[unknown IMAGE 1737984183564]
Think about how this plays out in HMM and LDS models.

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#### Flashcard 1738568240396

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#measure-theory #stochastics
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the Cantor set C∞ is a set of Lebesgue measure [...]
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
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The forward–backward algorithm computes the posterior marginals of all hidden state variables given [...]
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

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

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#eigen-analysis #spectral-theorem
Question
when applied to it, an eigenvector of a linear transformation only [...]
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

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

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

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[...] 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.

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:

#### Annotation 1760772099340

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

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 ∇.
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

#### Annotation 1760791497996

 #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}).}

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 ) {

#### Annotation 1760802245900

 A Hilbert curve is a continuous fractal space-filling curve

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

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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

#### Annotation 1760808799500

 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.

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

#### Annotation 1760814828812

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

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

#### Annotation 1760817712396

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

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

#### Annotation 1760819809548

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

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

#### Annotation 1760826101004

 [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

(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

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

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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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

#### Original toplevel document

(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,

#### Annotation 1760833703180

 #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.

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

#### Annotation 1760835800332

 #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.

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

#### Annotation 1760838159628

 #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.

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

#### Annotation 1760840518924

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

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

#### Annotation 1760842878220

 #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:

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

#### Annotation 1760844975372

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

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

#### Annotation 1760847596812

 #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

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

#### Annotation 1760849693964

 #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

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]

#### Annotation 1760853101836

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

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

#### Annotation 1760855198988

 #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.

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...]
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
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
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

#### 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

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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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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

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In calculus, foundations refers to the rigorous development of the subject from [...] .
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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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

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

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

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

#### Annotation 1760872762636

 #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

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

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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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In the 19th century, infinitesimals were replaced by [...]
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

#### 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

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Limits describe the value of a function at a certain input in terms of [...].
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

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

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

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

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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

#### Annotation 1760889015564

 #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

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derivative defined by limit considers [...] and extracts a consistent value for the exact point
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

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The tangent line is a limit of [...] just as the derivative is a limit of difference quotients.
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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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

#### Flashcard 1760895307020

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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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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

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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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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

#### Annotation 1760907365644

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

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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Es [...] agradable (He/She is not very kind).
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

#### Annotation 1760911822092

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

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

#### Annotation 1760913394956

 #spanish Empezamos a correr cuando vimos que llovía

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

#### Annotation 1760914967820

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

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

#### Annotation 1760916540684

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

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

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[...] decirle que me llame (Tell her to call me again).
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

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[...] correr cuando vimos que llovía
Empezamos a

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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

#### Flashcard 1760921521420

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

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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

#### Flashcard 1760923094284

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

#### Annotation 1760928075020

 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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#### Annotation 1760930434316

 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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#### Annotation 1760932007180

 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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#### Annotation 1760933580044

 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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#### Annotation 1760937250060

 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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#### Annotation 1760943279372

 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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#### Annotation 1760945638668

 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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#### Annotation 1760948260108

 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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#### Annotation 1760949832972

 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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#### Annotation 1760951405836

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

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#### Annotation 1760956386572

 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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#### Annotation 1760957959436

 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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#### Annotation 1760959532300

 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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#### Annotation 1760961105164

 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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#### Annotation 1760962678028

 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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#### Annotation 1760964250892

 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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#### Annotation 1760965823756

 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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#### Annotation 1760967396620

 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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#### Annotation 1760970542348

 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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#### Annotation 1760972115212

 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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#### Annotation 1760973688076

 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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#### Annotation 1760975260940

 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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#### Annotation 1760976833804

 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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#### Annotation 1760978406668

 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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#### Annotation 1760979979532

 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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#### Annotation 1760986270988

 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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#### Annotation 1760987843852

 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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#### Annotation 1760993086732

 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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#### Annotation 1760995708172

 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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#### Annotation 1760997805324

 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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#### Annotation 1760999378188

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

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#### Annotation 1761000951052

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

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#### Annotation 1761002523916

 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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#### Annotation 1761004096780

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

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#### Annotation 1761005669644

 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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#### Annotation 1761018252556

 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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#### Annotation 1761019825420

 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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#### Annotation 1761021398284

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

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#### Annotation 1761022971148

 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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#### Annotation 1761024544012

 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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#### Annotation 1761026116876

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

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#### Annotation 1761027689740

 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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#### Annotation 1761029262604

 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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#### Annotation 1761030835468

 train your brokers that you are a professional investor,

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#### Annotation 1761032408332

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