{* 3. Show that for the function f defined by setting x sin (1/y)+y sin (1/x), if xy#0 0 if xy=0, f(x, y) = 9 the two repeated limits do not exist, but lim (x, y)→(0, 0) f(x, y) exists.
{* 3. Show that for the function f defined by setting x sin (1/y)+y sin (1/x), if xy#0 0 if xy=0, f(x, y) = 9 the two repeated limits do not exist, but lim (x, y)→(0, 0) f(x, y) exists.
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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Show that f(x,y) limit exists at (0,0) using epsilon-delta.
Transcribed Image Text:3. Show that for the function f defined by setting
f(x, y)={ x sin (1/y)+y sin (1/x), if xy#0
0
if xy=0,
lim
(x, y)→(0, 0)
the two repeated limits do not exist, but
f(x, y) exists.
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