# How To Solve A Limit Using The Squeeze Theorem

## 1 Answer

\[-(x-1)^2\leq (x-1)^2\cos (\frac{1}{x}-1) \leq (x-1)^2.\]

Hence

\[0=\lim_{x\rightarrow 0}-(x-1)^2\leq \lim_{x\rightarrow 0} (x-1)^2\cos (\frac{1}{x}-1) \leq \lim_{x\rightarrow 0} (x-1)^2=0.\]

By the Squeeze Theorem

\[\lim_{x\rightarrow 0} (x-1)^2\cos (\frac{1}{x}-1)=0.\]

Erdos

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