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Q5. Let f: R² → R be defined by ea² +y² – 1 2² + y? - (x, y) # (0,0) f(x, y) = 0, (x, y) = (0,0). = e**+v² – 1. Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of g at (0,0). (a) Let g(x, y) Show all your work. (b) Using one of the corollaries to Taylor's Theorem (Section 8.3), prove that there exists a constant M > 0 so that

Q5. Let f: R² → R be defined by ea² +y² – 1 2² + y? - (x, y) # (0,0) f(x, y) = 0, (x, y) = (0,0). = e**+v² – 1. Find P2.(0,0)(x, y), the degree 2 Taylor polynomial of g at (0,0). (a) Let g(x, y) Show all your work. (b) Using one of the corollaries to Taylor's Theorem (Section 8.3), prove that there exists a constant M > 0 so that

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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Please do first two parts ( a and b)
Q5. Let f: R2 →R be defined by er² +y2 - 1 (x, y) # (0,0) f(x, y) = x² + y? 0, (x, y) = (0,0). (a) Let g(x, y) = e²²+v° – 1. Find P2,(0,0)(x, y), the degree 2 Taylor polynomial of g at (0,0). Show all your work. (b) Using one of the corollaries to Taylor's Theorem (Section 8.3), prove that there exists a constant M > 0 so that et² +y² - 1 - 1< M Vx2 + y? x² + y? for all (x, y) # (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (x,y)-(0,0) f(x, y).
Transcribed Image Text:Q5. Let f: R2 →R be defined by er² +y2 - 1 (x, y) # (0,0) f(x, y) = x² + y? 0, (x, y) = (0,0). (a) Let g(x, y) = e²²+v° – 1. Find P2,(0,0)(x, y), the degree 2 Taylor polynomial of g at (0,0). Show all your work. (b) Using one of the corollaries to Taylor's Theorem (Section 8.3), prove that there exists a constant M > 0 so that et² +y² - 1 - 1< M Vx2 + y? x² + y? for all (x, y) # (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (x,y)-(0,0) f(x, y).
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