find limit if it exists of function of two variables (x^2 * sin^2y) / (x^2 + 2y^2)

wolframAlpha claims the limit does not exist, but I'm unable to show how it doesn't. Evaluating the limit on the generalized line y=mx results in

evaluating along the curve y=x^2 gives

AFAICT, the limit /is/ 0. What am I missing?

Re: find limit if it exists of function of two variables (x^2 * sin^2y) / (x^2 + 2y^2

Quote:

Originally Posted by

**sgcb**
wolframAlpha claims the limit does not exist, but I'm unable to show how it doesn't. Evaluating the limit on the generalized line y=mx results in

evaluating along the curve y=x^2 gives

AFAICT, the limit /is/ 0. What am I missing?

I would say that I disagree. If you switch to polar coordinates we get

Using the above we can squeeze this using

Now by the squeeze theorem the limit must be zero.