13. Let g: R2 → R be a function given by xy x+y g(x, y) = { 0; if (x, y) = (0,0) (a) Show that g(x, y) is continuous at point (0,0) (b) Prove whether g(x, y) is differentiable at (0,0). = if (x, y) = (0,0)
13. Let g: R2 → R be a function given by xy x+y g(x, y) = { 0; if (x, y) = (0,0) (a) Show that g(x, y) is continuous at point (0,0) (b) Prove whether g(x, y) is differentiable at (0,0). = if (x, y) = (0,0)
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:13. Let g: R² → R be a function given by
xy
|x|+|y|
g(x, y) =
{
0;
if (x, y) = (0,0)
(a) Show that g(x, y) is continuous at point (0, 0)
(b) Prove whether g(x, y) is differentiable at (0,0).
=
if (x, y) = (0,0)
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