xy log(x² + y²), (x,y) # ɔ, (x,y) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
a) Is the function continuous at (0,0)?
b) Do the partial derivatives (D₁f)(0,0) and (D₂f)(0,0) exist?
c) For which u in ℝ² \ {0} does the directional derivative (D_uf)(0,0) exist?
d) Is f differentiable at (0,0)?
e) Determine the partial derivatives D₁f(x,y) and D₂f(x,y) for (x,y) ≠ (0,0).
f) Is f a C¹ function?
HINT: use the following standerd limit: see picture.
You could either solve these questions, or a detailed explanation
Thank you!
Transcribed Image Text:xylog(x² + y²), (x,y) ± (0,0),
f(x,y) :=
0,
(x, y) = (0,0).
Transcribed Image Text:lim sa log s = 0, Va > 0
80
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