Explanation Given information: Assume that a > b and L be the arc length of the ellipse ( x a ) 2 + ( y b ) 2 = 1 shown in the figure. there is no explicit formula for L . But is known that L = 4 b G ( k ) .Where k = 1 − a 2 b 2 . Calculation: Here, k = 1 − a 2 b 2 a = 4 and b = 5 k = 1 − 4 2 5 2 k = 9 25 k = 3 5 Now we find the L = 4 b G ( k ) L = 4 b G ( k ) L = 4 b G ( 3 5 ) ..... ( 1 ) But we have been given G ( k ) = π 2 − π 2 ∑ n = 1 ∞ ( 1 ⋅ 3 ⋅ ⋅ ⋅ ⋅ ( 2 n − 1 ) 2 2 ⋅ ⋅ ⋅ 4 ⋅ ( 2 n ) ) k 2 n 2 n − 1 From (1) L = 4 ( 5 ) [ π 2 − π 2 ∑ n = 1 ∞ ( 1 ⋅ 3 ⋅ ⋅ ⋅ ⋅ ( 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 11.7, Problem 91E

To determine

To calculate:

Use the first three terms by function G(k)=π2−π2∑n=1∞( 1⋅3 ⋅⋅⋅⋅ ( 2n−1 ) 2 2 ⋅⋅⋅4⋅( 2n ))k2n2n−1 and |k|<1 to estimate the L when a=4 and b=5

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Chapter 11.7, Problem 90E

Chapter 11.7, Problem 92E

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Chapter 11 Solutions

Calculus - Standalone book

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

Knowledge Booster

Use the first three terms by function G ( k ) = π 2 − π 2 ∑ n = 1 ∞ ( 1 ⋅ 3 ⋅ ⋅ ⋅ ⋅ ( 2 n − 1 ) 2 2 ⋅ ⋅ ⋅ 4 ⋅ ( 2 n ) ) k 2 n 2 n − 1 and | k | < 1 to estimate the L when a = 4 and b = 5

Solution Summary: The author explains how to calculate the L by using the first three terms by function G(k)=pi 2-

To calculate:

Use the first three terms by function G(k)=π2−π2∑n=1∞( 1⋅3 ⋅⋅⋅⋅ ( 2n−1 ) 2 2 ⋅⋅⋅4⋅( 2n ))k2n2n−1 and |k|<1 to estimate the L when a=4 and b=5

Want to see the full answer?

Chapter 11 Solutions

Use the first three terms by function G ( k ) = π 2 − π 2 ∑ n = 1 ∞ ( 1 ⋅ 3 ⋅ ⋅ ⋅ ⋅ ( 2 n − 1 ) 2 2 ⋅ ⋅ ⋅ 4 ⋅ ( 2 n ) ) k 2 n 2 n − 1 and | k | &lt; 1 to estimate the L when a = 4 and b = 5

Solution Summary: The author explains how to calculate the L by using the first three terms by function G(k)=pi 2-

To calculate: Use the first three terms by function G(k)=π2−π2∑n=1∞( 1⋅3 ⋅⋅⋅⋅ ( 2n−1 ) 2 2 ⋅⋅⋅4⋅( 2n ))k2n2n−1 and |k|<1 to estimate the L when a=4 and b=5

Want to see the full answer?

Chapter 11 Solutions

Use the first three terms by function G ( k ) = π 2 − π 2 ∑ n = 1 ∞ ( 1 ⋅ 3 ⋅ ⋅ ⋅ ⋅ ( 2 n − 1 ) 2 2 ⋅ ⋅ ⋅ 4 ⋅ ( 2 n ) ) k 2 n 2 n − 1 and | k | < 1 to estimate the L when a = 4 and b = 5

To calculate:

Use the first three terms by function G(k)=π2−π2∑n=1∞( 1⋅3 ⋅⋅⋅⋅ ( 2n−1 ) 2 2 ⋅⋅⋅4⋅( 2n ))k2n2n−1 and |k|<1 to estimate the L when a=4 and b=5