<s>[INST] Finding the limit of a function with 2 variables Please help to solve the limit.
$$\lim_{(x,y)\rightarrow(0,0)}\dfrac{x^3+y^3}{x^2+y^2}$$
I tried to solve it but...
$$x:=0 \Rightarrow \dfrac{x^3+y^3}{x^2+y^2} = y$$
$$y:=0 \Rightarrow \dfrac{x^3+y^3}{x^2+y^2} = x$$
 [/INST] $$x:=r\cos\theta$$
$$y:=r\sin\theta$$
$$\lim_{(x,y)\to(0,0)}\frac{x^3+y^3}{x^2+y^2}=\lim_{r\to0}\frac{r^3\cos^3\theta+r^3\sin^3\theta}{r^2}=\lim_{r\to0}r(\cos^3\theta+\sin^3\theta)=0$$
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