Encontrar $\displaystyle\lim_{x \rightarrow 0_+} \dfrac{x}{\sqrt{1 - \cos x}}$.

$\dfrac{x}{\sqrt{1 - \cos x}} \overset{x \in \left]0, \dfrac{\pi}{2}\right[}{=} \dfrac{x\sqrt{1 + \cos x}}{\sin x}$

$\displaystyle\lim_{x \rightarrow 0_+} \dfrac{x\sqrt{1 + \cos x}}{\sin x} = \cancelto{1}{\displaystyle\lim_{x \rightarrow 0_+} \dfrac{x}{\sin x}} \cdot \displaystyle\lim_{x \rightarrow 0_+} \sqrt{1 + \cos x}= \sqrt{2}$