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the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output)[1] at point a is defined as[2] using functions and their derivatives meaning in words: <span>It is thus the ratio of the relative (percentage) change in the function's output \(f(a)\) with respect to the relative change in its input \(a\), for infinitesimal changes from a point . <span><body><html>

er:filter:minify-css:7:3904d24a08aa08f6a68dc338f9be277e */ Elasticity of a function From Wikipedia, the free encyclopedia Jump to: navigation, search <span>In mathematics, the elasticity or point elasticity of a positive differentiable function f of a positive variable (positive input, positive output)[1] at point a is defined as[2] or equivalently It is thus the ratio of the relative (percentage) change in the function's output with respect to the relative change in its input , for infinitesimal changes from a point . Equivalently, it is the ratio of the infinitesimal change of the logarithm of a function with respect to the infinitesimal change of the logarithm of the argument. The elasticity of a function is a constant if and only if the function has the form for a constant . The elasticity at a point is the limit of the arc elasticity between two points as

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ction contains examples and problems to boost understanding in the usage of the difference of squares identity: \(a^2-b^2=(a+b)(a-b)\). Here are the examples to learn the usage of the identity. <span>Rewrite \(5^2-2^2\) as a product. We have \[5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square\] Calculate \(299\times 301\). You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

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In Whipple’s disease, 87% are males, usually white and middle- aged. It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopat

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In Whipple’s disease, 87% are males, usually white and middle- aged. It presents with arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopathy and involvement of the heart, lung, join

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arthritis and arthralgia, progressing over years to weight loss and diarrhoea with abdominal pain, systemic symptoms of fever and weight loss. Peripheral lymphadenopathy and involvement of the <span>heart, lung, joints and brain occur, simulating many neurological conditions <span>

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in 10% of cases of IBD causing colitis a definitive diagnosis of either UC or CD is not possible and the diagnosis is termed colitis of undetermined type and etiology (CUTE).

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Jewish people are more prone to inflammatory bowel disease than any other ethnic group.

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Crohn's Disease and Ulcerative colitis are complex polygenic diseases and having a positive family history is the largest independent risk factor.

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ave an account? Log in here. Quiz Solving Identity Equations Relevant For... Algebra > Polynomial Arithmetic Ram Mohith , Beakal Tiliksew , Mahindra Jain , and 1 other Jimin Khim contributed <span>An identity equation is an equation that is always true for any value substituted into the variable. \(_\square\) For example, \(2(x+1)=2x+2\) is an identity equation. One way of checking is by simplifying the equation. \[\begin{align} 2(x+1)&=2x+2\\ 2x+2&=2x+2\\ 2&=2. \end{align}\] \(2

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ue View solutions What is Note: Try it without using a calculator. Correct! The answer is 1. 74% of people got this right. Continue View solutions Don't use a calculator! Further Extension Edit <span>Since the two factors are different by , the factors will always have the same parity. That is, if is even then must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: Problem Solving Edit The examples and problems in this sections are a bit hard

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not just learn once but you will repeat the material optimally (as in SuperMemo). The 20 rules of formulating knowledge in learning Do not learn if you do not understand Trying to learn things y<span>ou do not understand may seem like an utmost nonsense. Still, an amazing proportion of students commit the offence of learning without comprehension. Very often they have no other choice! The quality of many textbooks or lecture scripts is deplorable while examination deadlines are unmovable. If you are not a speaker of German, it is still possible to learn

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nce of learning without comprehension. Very often they have no other choice! The quality of many textbooks or lecture scripts is deplorable while examination deadlines are unmovable. If you are <span>not a speaker of German, it is still possible to learn a history textbook in German. The book can be crammed word for word. However, the time needed for such "blind learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history

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learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history book <span>example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". Learn before you memorize Before you proceed with memorizing individual facts and rules, you need to build an overall picture of the learned knowledge. Only when individual pieces fit t

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example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day".

learning" is astronomical. Even more important: The value of such knowledge is negligible. If you cram a German book on history, you will still know nothing of history. The German history book <span>example is an extreme. However, the materials you learn may often seem well structured and you may tend to blame yourself for lack of comprehension. Soon you may pollute your learning process with a great deal of useless material that treacherously makes you believe "it will be useful some day". Learn before you memorize Before you proceed with memorizing individual facts and rules, you need to build an overall picture of the learned knowledge. Only when individual pieces fit t

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e lame. If you know Bruce Willis is dead, don’t watch the 6th Sense. But textbooks are rarely building to a suspenseful twist at the end. I promise. I’ve read a lot. They don’t come with surpris<span>e endings. “And then, Abraham Lincoln dodged the bullet!” Yep, that’s never going to be in a textbook. Want to try this strategy? Try reading your textbook chapter in this order: Go to the questions at th

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Rewrite 52−22 as a product. We have 52−22=(5−2)×(5+2)=3×7. □

ction contains examples and problems to boost understanding in the usage of the difference of squares identity: \(a^2-b^2=(a+b)(a-b)\). Here are the examples to learn the usage of the identity. <span>Rewrite \(5^2-2^2\) as a product. We have \[5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square\] Calculate \(299\times 301\). You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

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lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Since the two factors are different by 2b , the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 square

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the differ

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares.

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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Rewrite 52−22 as a product. We have 52−22=(5−2)×(5+2)=3×7.

ction contains examples and problems to boost understanding in the usage of the difference of squares identity: \(a^2-b^2=(a+b)(a-b)\). Here are the examples to learn the usage of the identity. <span>Rewrite \(5^2-2^2\) as a product. We have \[5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square\] Calculate \(299\times 301\). You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if a−b is even then a+b must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not

lor{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ? \] Don't use a calculator! Further Extension <span>Since the two factors are different by \(2b\), the factors will always have the same parity. That is, if \(a-b\) is even then \(a+b\) must also be even, so the product is divisible by four. Or neither are divisible by 2, so the product is odd. This implies that numbers which are multiple of 2 but not 4 cannot be expressed as the difference of 2 squares. The product of two differences of two squares is itself a difference of two squares in two different ways: \[\begin{array} { l l l } \left(a^2-b^2\right)\left(c^2-d^2\right) &= (ac)

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