Answer
1
Work Step by Step
See The Squeeze Theorem, p.69:
If $f(x) \leq g(x) \leq h(x)$, and $\displaystyle \lim_{x\rightarrow a}f(x)= \displaystyle \lim_{x\rightarrow a}h(x)=L,$
then $\displaystyle \lim_{x\rightarrow a}g(x)=L.$
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$\displaystyle \lim_{x\rightarrow 1}(2\mathrm{x}-1)=1$
$\displaystyle \lim_{x\rightarrow 1}(x^{2})=1$
so, by the squeeze theorem, $\displaystyle \lim_{x\rightarrow 1}f(x)=1$
