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Q. $\lim_{x \to 2} \frac {2x^2-5x+2} {x^2 -3x +2} $

Solution:

$\lim_{x\to2} \frac{2x^{2}-5x +2}{x^{2}-3x +2} = \lim_{x\to2} \frac{\left(x-2\right)\left(2x-1\right)}{\left(x-2\right)\left(x-1\right)} $
$\lim_{x\to2} \frac{2x-1}{x-1}=\frac{4-1}{2-1}=3$