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

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- Jun 7th 2012, 06:55 AMsluggerbrothevaluate limit using squeeze theorem
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

any tips on keying in math symbols??? - Jun 7th 2012, 07:01 AMReckonerRe: evaluate limit using squeeze theorem
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, $\displaystyle \lim_{x\to2}f(x)=\mathrm?$