Final answer to the problem
$1$
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Step-by-step Solution
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- Solve using direct substitution
- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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1
Apply the power rule for limits: $\lim_{x\to a}\left(f(x)\right)^n=\left(\lim_{x\to a}f(x)\right)^n$
${\left(\lim_{x\to\infty }\left(\cos\left(\frac{1}{x}\right)\right)\right)}^2$
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${\left(\lim_{x\to\infty }\left(\cos\left(\frac{1}{x}\right)\right)\right)}^2$
Learn how to solve 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 . The cosine of 0 equals 1.
Final answer to the problem
$1$
