Multivariable Limit

  • #1

Homework Statement



Find that the limit exists, or show that the limit does not exist.

lim (x,y) --> (0,0) of (x^2 * sin^2y)/(x^2 + 2y^2)


Homework Equations


??

The Attempt at a Solution



i used the lines x=0 y=0 and both times got the limit 0 so i attempted to prove the limit exists

I attempted to use the limit definition,

1 >= |sin^2| >= 0
x^2 + 2y^2 >= x^2
x^2+2y^2 >= x^2sin^2y
|x^2sin^2y/x^2+2y^2| <= 1

uhmm.... Im not sure what do after this or really what the heck im doing. HELP? :)
 

Answers and Replies

  • #2
104
0
You are forgetting to check one last condition before proving that the limit exist! Not sure if it would do anything but try plugging x = y and y = x. If this checks out ( = 0) then you can be sure that the limit exist and try to prove it.
 

Related Threads on Multivariable Limit

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
10
Views
834
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
20
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
1K
Top