Continuity of a two variable function
The question is :
Prove that f is continuous at the point (0,0) where f is
f(x,y)= ysin(1/x) , when x is not equal to zero
0 , when x=0.
I have to prove this using the epsilon-delta definition of limit. Can't figure out how to do that ?
Can somebody please explain the procedure .
Re: Continuity of a two variable function
Do you not know what the "epsilon-delta definition of a limit? For a function of two variables, you must show
"For any there exist such that if then < \epsilon[/tex].
Here, your function is and you want the limit to be the value of the function, 0. So you want to get for x and y sufficiently small. I would use the fact that because for any x not equal to 0.