Answer
$1$
Work Step by Step
The polar-coordinates are defined as: $x= r \cos \theta , y = r \sin \theta$ and $r^2=x^2+y^2$
$ \lim\limits_{(x,y) \to (0,0) } f(x,y)=\lim\limits_{(x,y) \to (0,0) } \cos \dfrac{x^3-xy^2}{x^2+y^2}$
or, $=\lim\limits_{r \to 0} \cos (\dfrac{ r^3 \cos^3 \theta- r^3 \sin^3 \theta}{r^2})$
or, $=\cos (0)$
or, $=1$
