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ez+y? 1 - 1 < MVx2 + y? x2 + y? for all (x, y) (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (r,y)-(0,0) f(x, y).

ez+y? 1 - 1 < MVx2 + y? x2 + y? for all (x, y) (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (r,y)-(0,0) f(x, y).

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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Need only part c
Q5. Let f: R² → R be defined by er2 +y? – 1 (x, y) # (0,0) f(x, y) = x2 + y? (x, y) = (0,0). (a) Let g(x, y) = e"²+y° – 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 er2 +y? - 1 - 1 < MVx2 + y? x2 + y? for all (x, y) # (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (r,y)→(0,0) f(x, y).
Transcribed Image Text:Q5. Let f: R² → R be defined by er2 +y? – 1 (x, y) # (0,0) f(x, y) = x2 + y? (x, y) = (0,0). (a) Let g(x, y) = e"²+y° – 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 er2 +y? - 1 - 1 < MVx2 + y? x2 + y? for all (x, y) # (0,0) in some neighborhoud of (0, 0). (c) Using part (b), evaluate lim (r,y)→(0,0) f(x, y).
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