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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Question
Transcribed Image Text:2. Let f : R² → R given by
x5
f(x, y) =
for
xª + 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 derivatives
Dıf(0,0) = əx
fe
-(0,0).
ду
-(0,0)
fe
and
D2f(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.
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