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Let f : R? → R be defined as follows: if (r, y) + (0,0) f(r, u) = else. (a) Do the partial derivatives of f exist in (0, 0)? (b) Does Da)f(0,0), i.e. the directional derivative of f in direction (1,1) in the point (0,0), exist? (c) Is f differentiable in (0,0)? Tip: Remember the definition of the partial and directional derivatives. 3

Let f : R? → R be defined as follows: if (r, y) + (0,0) f(r, u) = else. (a) Do the partial derivatives of f exist in (0, 0)? (b) Does Da)f(0,0), i.e. the directional derivative of f in direction (1,1) in the point (0,0), exist? (c) Is f differentiable in (0,0)? Tip: Remember the definition of the partial and directional derivatives. 3

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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Problem 7 Let f : R? → R be defined as follows: if (r, y) + (0,0) f(r, y) = else. (a) Do the partial derivatives of f exist in (0, 0)? (b) Does Duyf(0,0), i.e. the directional derivative of f in direction (1,1) in the point (0, 0), exist? (c) Is f differentiable in (0,0)? Tip: Remember the definition of the partial and directional derivatives. 3
Transcribed Image Text:Problem 7 Let f : R? → R be defined as follows: if (r, y) + (0,0) f(r, y) = else. (a) Do the partial derivatives of f exist in (0, 0)? (b) Does Duyf(0,0), i.e. the directional derivative of f in direction (1,1) in the point (0, 0), exist? (c) Is f differentiable in (0,0)? Tip: Remember the definition of the partial and directional derivatives. 3
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