Explanation G is a coordinate transformation from x y -plane to u v -plane then G ( u , v ) = ( x , y ) ---------------- (i) Given: G ( u , v ) = ( u e v , e u ) ---------- (ii) Comparing (i) and (ii), x = u e v ; y = e u Calculation: Jacobian of the transformation is J ( u , v ) = ∂ ( x , y ) ∂ ( u , v ) = | ∂ x ∂ u ∂ x ∂ v ∂ y ∂ u ∂ y ∂ v | --------- (iii) Where ∂ x ∂ u , ∂ x ∂ v , ∂ y ∂ u , ∂ y ∂ v are first order partial derivatives. ∂ x ∂ u = ∂ ∂ u ( u e v ) = e v ∂ ∂ u ( u ) = e v ( 1 ) = e v [While differentiating partially with respect to u treat v as constant] ∂ x ∂ ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known …

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Chapter 16.6, Problem 18E

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The Jacobian

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Chapter 16.6, Problem 17E

Chapter 16.6, Problem 19E

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Question 3. the given integral is convergent or divergent: Use the comparison test to determine whether or not * sin*(x + 1) 7x3 (a) |. d.x g8 + x4 + 1 -dx (b) 2.x4 + x + 1

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Chapter 16 Solutions

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The Jacobian

Solution Summary: The author explains that the Jacobian solution is J = e u + v.

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Chapter 16 Solutions