# Thread: evaluate limit using squeeze theorem

1. ## evaluate 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

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2. ## Re: evaluate limit using squeeze theorem

Originally Posted by sluggerbroth
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 $2x-1\leq f(x)\leq x^2-2x+3$ for all $x\neq2$.

$\lim_{x\to2}\left(2x-1\right) = 3$ and $\lim_{x\to2}\left(x^2-2x+3\right) = 3$. So, by the Squeeze Theorem, $\lim_{x\to2}f(x)=\mathrm?$