## Calculus 8th Edition

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 $\displaystyle \lim_{x\rightarrow a}g(x)=L.$ ------ $\displaystyle \lim_{x\rightarrow 1}(2\mathrm{x}-1)=1$ $\displaystyle \lim_{x\rightarrow 1}(x^{2})=1$ so, by the squeeze theorem, $\displaystyle \lim_{x\rightarrow 1}f(x)=1$