(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I must say if the function is continuous in the point (0,0). Which is [tex]\displaystyle\lim_{(x,y) \to{(0,0)}}{f(x,y)}=f(0,0)[/tex]

The function:

[tex]f(x,y)=\begin{Bmatrix} (x+y)^2\sin(\displaystyle\frac{\pi}{x^2+y^2}) & \mbox{ if }& y\neq{-x}\\1 & \mbox{if}& y=-x\end{matrix}[/tex]

I think its not continuous at any point, cause for any point I would ever have a disk of discontinuous points, but I must prove it. And I wanted to do so using limits, which I think is the only way to do it.

[tex]\displaystyle\lim_{(x,y) \to{(0,0)}}{(x+y)^2\sin(\displaystyle\frac{\pi}{x^2+y^2})}[/tex]

What should I do? should I use trajectories? the limit seems to exist, as the sin oscilates between -1 and 1, and the other part tends to zero.

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# Homework Help: Continuity in Calc III problem

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