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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

I have attempted to solve this by letting y=x giving me

lim (x^2*sin^2(x))/(x^2+2x^2) = lim x^2sin^2(x)/3x^2 = sin^2(x)/3 = 0

(x,x)->(0,0) (x,x)->(0,0)

And by letting both x and y = 0, both of which gave me the limit as being equal to 0 (left out equation, but can add in case I'm doing something wrong). The problem is that while all of these have given me a limit equal to zero, I don't know when I'm done and can say that the limit equals zero. We haven't gone over substituting in polar coordinates and when I tried to see how to do that I ended up confusing myself. Any easy to follow steps? (I did look back at other topics with the same problems, but wasn't able to work it out)