Can you find the limit if it exists, or show that it doesn't?

Question

no i'm not necessarily just looking for the answer, but seriously how to do it and where to start. the problem is this:

limit (x,y)-->(0,0) (x^2+(siny)^2)/(2x^2+y^2)

thanks!

Answer 1

To show that it doesn't exist, look at the path where x=0 and y moves to zero. The problem reduces to:

sin(y)/y^2

You can use L'Hospital's rule to show that this limit does not exist.

Answer 2

it doesnt exist