2. Let f : R² → R given byx5f(x, y) =forxª + y²(x, y) # (0,0)and f(0,0) = 0.(a) Is f continuous at (0,0)? To get full marks you must justify your answer.(b) Compute the partial derivativesDıf(0,0) = əxfe-(0,0).ду-(0,0)feandD2f(0,0) =(c) Let u =(v, w) with v² + w² = 1. Determine the directional derivative Duƒ(0,0).(d) Is f differentiable at (0, 0)? To get full marks you must justify your answer.

Answered: Image /qna-images/answer/7861d2c6-3232-4969-a771-7255243bc00b.jpg

2. Let f : R? → R given by f(x, y) = x4 for (x, y) # (0, 0) %3D + y? and f(0,0) = 0. %3D (a) Is f continuous at (0,0)? To get full marks you must justify your answer. (b) Compute the partial derivatives fe and Daf(0,0) = (0,0). Dif(0,0) -(0,0) dy (c) Let u = (v, w) with v² + w² = 1. Determine the directional derivative Duf(0,0). (d) Is f differentiable at (0, 0)? To get full marks you must justify your answer.

2. Let f : R? → R given by f(x, y) = x4 for (x, y) # (0, 0) %3D + y? and f(0,0) = 0. %3D (a) Is f continuous at (0,0)? To get full marks you must justify your answer. (b) Compute the partial derivatives fe and Daf(0,0) = (0,0). Dif(0,0) -(0,0) dy (c) Let u = (v, w) with v² + w² = 1. Determine the directional derivative Duf(0,0). (d) Is f differentiable at (0, 0)? To get full marks you must justify your answer.

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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