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Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$
Learn how to solve limits to infinity problems step by step online.
${\left(\lim_{x\to\infty }\left(\cos\left(\frac{1}{x}\right)\right)\right)}^2$
Learn how to solve limits to infinity problems step by step online. Find the limit of cos(1/x)^2 as x approaches infinity. Apply the power rule for limits: \lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n. Because cosine is a continuous function, we can bring the limit inside of the cosine. Evaluate the limit \lim_{x\to\infty }\left(\frac{1}{x}\right) by replacing all occurrences of x by \infty . Any expression divided by infinity is equal to zero.