Find the limits for this function Find the limits
$ \lim_{x\to 0} \frac {x^2 sin^2 (x)} {x^2 - sin^2 (x)}$

$\lim\limits_{x\to 0}\dfrac{x^2 \sin^2 x}{x^2-\sin^2 x} = \lim\limits_{x\to 0}\dfrac{x^2}{x^2\csc^2 x-1} = \lim\limits_{x\to 0}\dfrac{x^2}{(x\csc x-1)(x\csc x +1)} = \dfrac 1 2\lim\limits_{x\to 0} \dfrac{x^2}{x\csc x-1}$
Then apply l'Hospital's Rule ($\times 2$).
