Answer to Question #239398 in Calculus for sam

Question

Evaluate the limit $\displaystyle{\lim\limits_{\theta \to 0} \dfrac{\sin{(\theta^2)}}{\theta}}$ using the l'Hopital's Rule.

Answer 1

$\lim\limits_{\theta\to0}{sin(\theta^2)\over \theta}$

$=\lim\limits_{\theta\to0}({f'(sin(\theta^2))\over f'( \theta)})$

$=\lim\limits_{\theta\to0}({2.\theta.cos(\theta^2)\over 1})$

$=({2.0.cos(0^2)\over 1})={0\over 1}=0$