TeX source:
\begin{align} L & = \lim_{|x| \to \infty}\ \frac{\cos \frac 1x \cdot \frac{-1}{x^2}}{\frac{-1}{x^2}} \\ & = \lim_{|x| \to \infty} {\cos\frac 1x} \cdot \frac{-1}{x^2} \cdot \frac{x^2}{-1} \\ & = \cos\frac{1}{\infty} = \cos 0 = 1 \end{align}