I tried using L'Hospital's rule to find the limit as $x$ tends to $0$ for the following function:
$$f(x) = \frac{(1 - \cos x)^{1.5}}{x - \sin x}$$ I tried differentiating the top and the bottom and I can do it many times but it still gives the denominator with zero meaning I have to differentiate again and again (mainly because a $(1 - \cos x)^{0.5}$ always manages to find its way into the numerator.)
Is there a better way of solving this limit question?