Find the limit: _ x 2 [ x^ 3 -2 x^ 2 x^ 2 -5 x+6 ] - Vidyadip

Question

Find the limit: $\lim \limits_{x \rightarrow 2}\left[\frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}\right]$

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Answer

Evaluating the function at 2, we get it of the form $\frac{0}{0}$
Therefore, we have,
$\lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}}{x^{2}-5 x+6}=\lim _{x \rightarrow 2} \frac{x^{2}(x-2)}{(x-2)(x-3)}$
$=\lim _{x \rightarrow 2} \frac{x^{2}}{(x-3)}=\frac{(2)^{2}}{2-3}=\frac{4}{-1}=-4$

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