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Question

Mathematics Question on Limits

lim⁡x→22x2−5x+2x2−3x+2\lim_{x \to 2} \frac {2x^2-5x+2} {x^2 -3x +2}

A

1

B

2

C

3

D

8

Answer

3

Explanation

Solution

lim⁡x→22x2−5x+2x2−3x+2=lim⁡x→2(x−2)(2x−1)(x−2)(x−1)\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→22x−1x−1=4−12−1=3\lim_{x\to2} \frac{2x-1}{x-1}=\frac{4-1}{2-1}=3