Consider the functional S[y] = =ffdx [₁ = dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y is a continuously differentiable function for 1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2, and let e be a constant. Let A = S[y+ ch] - S[y]. (a) Show that x²h' 24h2 A = c ² da 4²² - ² ² dx + 22/7² +0(8³). dx 1 1 + x²y' 2 (1+x²y')²

Consider the functional S[y] = =ffdx [₁ = dx ln(1 + x²y'), y(1) = 0, y(2) = A, where A is a constant and y is a continuously differentiable function for 1 ≤ x ≤ 2. Let h be a continuously differentiable function for 1 ≤ x ≤ 2, and let e be a constant. Let A = S[y+ ch] - S[y]. (a) Show that x²h' 24h2 A = c ² da 4²² - ² ² dx + 22/7² +0(8³). dx 1 1 + x²y' 2 (1+x²y')²

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 48E

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