I was trying to prove that the limit of the function $\frac{\sin(x^2+y^2)}{x^2+y^2}$ is 1 as we apply the limit $(x,y)\rightarrow (0,0)$. I took the polar form for the variables $x$ and $y$ and then applied the limit $r\rightarrow 0$ and finally answer is $1$. But I am unable to prove the same with the help of $\epsilon -\delta$ method. Can anyone help me in solving the same. Following is my attempt. Please feel free to rectify the proof.
