Evaluate the following Limits: _ x 2 [(x-2) 2 x^2-7 x+6 ] - Vidyadip

Question

Evaluate the following Limits:$\lim _{x \rightarrow 2}\left[\frac{(x-2)}{2 x^2-7 x+6}\right]$

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Answer

$ \lim _{x \rightarrow 2}\left(\frac{x-2}{2 x^2-7 x+6}\right)$
$ =\lim _{x \rightarrow 2} \frac{x-2}{(x-2)(2 x-3)}$
$ =\lim _{x \rightarrow 2} \frac{1}{2 x-3} \ldots [\text { As } x \rightarrow 2, x \neq 2 \therefore x-2 \neq 0]$
$ =\frac{1 \text { }}{2(2)-3}$
$ =1$

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