Answer
\[ = 0\]
Work Step by Step
\[\begin{gathered}
\mathop {\lim }\limits_{x \to \infty } \,\,\frac{{\cos x}}{x} \hfill \\
\hfill \\
evaluate\,\,\,x = \infty \hfill \\
\hfill \\
= \mathop {\lim }\limits_{x \to \infty } \,\,\frac{{\cos \infty }}{\infty } \hfill \\
\hfill \\
\,\,where\,\,\cos \,\,\infty \,\,oscillates\,between\,\,\,\left( { - 1\,\,to\,\,1} \right) \hfill \\
\hfill \\
then \hfill \\
\hfill \\
= \frac{a}{\infty } \hfill \\
\hfill \\
= 0 \hfill \\
\end{gathered} \]
