Answer
$$1$$
Work Step by Step
Given $$\lim_{x\to\infty}\cos \left(\frac{1}{x}\right) $$
Then
\begin{align*}
\lim_{x\to\infty}\cos \left(\frac{1}{x}\right) &=\cos \left(\lim_{x\to\infty}\frac{1}{x}\right) \\
&=\cos (0)\\
&=1
\end{align*}
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