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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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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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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