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2. Find the quadratic approximations at (0, 0) for (a) f(x, y) = e*+ (xy − 1) (b) f(x, y) = etey (c) f(x, y) = ln(1 + x² + y²)

2. Find the quadratic approximations at (0, 0) for (a) f(x, y) = e*+ (xy − 1) (b) f(x, y) = etey (c) f(x, y) = ln(1 + x² + y²)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you answer this question using Taylor's formula? Please answer this on pencil and paper.

THEOREM 2.6.1 (TAYLOR'S FORMULA) If f is n + 1 times differentiable in an interval that contains a and x, then f(n) (a) (x-a)" + f(n+1) (c) (n + 1)! n! f'(a) f(x) = f(a)+ (x- 1! for some number c between a and x. c-a)+...+ (x-a)¹+1
Transcribed Image Text:THEOREM 2.6.1 (TAYLOR'S FORMULA) If f is n + 1 times differentiable in an interval that contains a and x, then f(n) (a) (x-a)" + f(n+1) (c) (n + 1)! n! f'(a) f(x) = f(a)+ (x- 1! for some number c between a and x. c-a)+...+ (x-a)¹+1
2. Find the quadratic approximations at (0, 0) for (a) f(x, y) = e*+(xy − 1) (b) f(x, y) = etey (c) f(x, y) = ln(1 + x² + y²)
Transcribed Image Text:2. Find the quadratic approximations at (0, 0) for (a) f(x, y) = e*+(xy − 1) (b) f(x, y) = etey (c) f(x, y) = ln(1 + x² + y²)
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