lim f(x) as x goes to 2 where 2x-1 (< or equal) f(x) (< or equal) x^2-2x+3, x does not = 2
We have $\displaystyle 2x-1\leq f(x)\leq x^2-2x+3$ for all $\displaystyle x\neq2$.
$\displaystyle \lim_{x\to2}\left(2x-1\right) = 3$ and $\displaystyle \lim_{x\to2}\left(x^2-2x+3\right) = 3$. So, by the Squeeze Theorem, $\displaystyle \lim_{x\to2}f(x)=\mathrm?$