Consider the function: 3.3 x²+yⓇ 0 if (x, y) = (0,0) if (x, y) = (0,0) a - Determine if f is continuous at the origin. b - Determine the directional derivatives at the origin. c- Determine if f is differentiable at the origin. d - Describe possible implications between directional derivatives, continuity, and differentiability.
Consider the function: 3.3 x²+yⓇ 0 if (x, y) = (0,0) if (x, y) = (0,0) a - Determine if f is continuous at the origin. b - Determine the directional derivatives at the origin. c- Determine if f is differentiable at the origin. d - Describe possible implications between directional derivatives, continuity, and differentiability.
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:Consider the function:
3.3
x*y*
x²+y6
0
if (x, y) = (0,0)
if (x, y) = (0,0)
a - Determine if f is continuous at the origin.
b - Determine the directional derivatives at the origin.
c - Determine if f is differentiable at the origin.
d - Describe possible implications between directional derivatives, continuity, and
differentiability.
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