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Question 5 Suppose that y(x) is defined implicitly as a function of x by the following equa- tion: x² + 5x²y² + y² = 2 Note that (x, y) =(,1) satisfies this equation. Assume a>0 and y > 0. i. Find an expression for dy/dx and evaluate it at (,1). ii. Find an expression for dy/de² and evaluate it at (,1). iii. Find a second order Taylor approximation of y(x) about x = iv. Graph the approximating function you derived in iii.

Question 5 Suppose that y(x) is defined implicitly as a function of x by the following equa- tion: x² + 5x²y² + y² = 2 Note that (x, y) =(,1) satisfies this equation. Assume a>0 and y > 0. i. Find an expression for dy/dx and evaluate it at (,1). ii. Find an expression for dy/de² and evaluate it at (,1). iii. Find a second order Taylor approximation of y(x) about x = iv. Graph the approximating function you derived in iii.

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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Question 5 Suppose that y(x) is defined implicitly as a function of x by the following equa- tion: x² + 5x²y² + y² = 2 Note that (x,y)=(,1) satisfies this equation. Assume a > 0 and y > 0. i. Find an expression for dy/dx and evaluate it at (,1). ii. Find an expression for y/da² and evaluate it at (,1). iii. Find a second order Taylor approximation of y(x) about x = iv. Graph the approximating function you derived in iii.
Transcribed Image Text:Question 5 Suppose that y(x) is defined implicitly as a function of x by the following equa- tion: x² + 5x²y² + y² = 2 Note that (x,y)=(,1) satisfies this equation. Assume a > 0 and y > 0. i. Find an expression for dy/dx and evaluate it at (,1). ii. Find an expression for y/da² and evaluate it at (,1). iii. Find a second order Taylor approximation of y(x) about x = iv. Graph the approximating function you derived in iii.
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