1. Let a, ß EN. Let f(x, y) = af дх rªy³ x² + y² for (x, y) = (0,0). that f is continuous on R². Compute the partial derivatives of f at each point of R². Analogously, prove that or a + ß> 3. we assume in addition Prove that admits a limit at (0, 0) if and only if a = 1 ora+ß > 3. af admits a limit at (0, 0) if and only if 3 = 1 c) Assume a +3> 3. Is f differentiable on R²?
1. Let a, ß EN. Let f(x, y) = af дх rªy³ x² + y² for (x, y) = (0,0). that f is continuous on R². Compute the partial derivatives of f at each point of R². Analogously, prove that or a + ß> 3. we assume in addition Prove that admits a limit at (0, 0) if and only if a = 1 ora+ß > 3. af admits a limit at (0, 0) if and only if 3 = 1 c) Assume a +3> 3. Is f differentiable on R²?
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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Transcribed Image Text:1.
Let a, ß E N. Let f(x, y) =
Prove that
af
дх
rªy³
x² + y²
that f is continuous on R².
Compute the partial derivatives of f at each point of R².
for (x, y) = (0,0).
Analogously, prove that of
ду
or a + ß> 3.
we assume in addition
admits a limit at (0, 0) if and only if a = 1 ora+ß > 3.
admits a limit at (0, 0) if and only if 3 = 1
c) Assume a +3> 3. Is f differentiable on R²?
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