Let f : R2 → R be a function given by x² -y? 2+y² { if (x, y) # (0,0), f(x, y) : if (x, y) = (0,0). Using definitions of partial derivatives, show whether f(x, y) is differentiable at point (0,0). [6]

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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)-10 if (7,y) = (0,0).
Let f : R2 → R be a function given by
x² -y?
{
xy
if (x, y) # (0,0),
f(x, y) =
if (x, y) = (0,0).
Using definitions of partial derivatives, show whether f(x, y) is differentiable at
point (0,0).
[6]
Transcribed Image Text:)-10 if (7,y) = (0,0). Let f : R2 → R be a function given by x² -y? { xy if (x, y) # (0,0), f(x, y) = if (x, y) = (0,0). Using definitions of partial derivatives, show whether f(x, y) is differentiable at point (0,0). [6]
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