[math]\lim_{(x,y)\to(0,0)}\frac{x^4+y^4}{x^2+y^2}\cdot\sin\left(\frac{1}{x}\right)\\\\-1\leq\sin\left(\frac{1}{x}\right)\leq1,\,\,\\\text{so using Squeeze theorem we got:}\\\\0\leftarrow-\frac{x^4+y^4}{x^2+y^2}\leq\frac{x^4+y^4}{x^2+y^2}\cdot\sin\left(\frac{1}{x}\right)\leq\frac{x^4+y^4}{x^2+y^2}\rightarrow 0\\\\\Rightarrow \lim_{(x,y)\to(0,0)}\frac{x^4+y^4}{x^2+y^2}\cdot\sin\left(\frac{1}{x}\right)=0\\\\\text{but wolfram says that limit doesn't exist, where is my mistake and how to solve it another way?}[/math]