Evaluate the following limits : _ z 2 [z^2-5 z+6 z^2-4 ] - Vidyadip

Question

Evaluate the following limits : $\lim _{z \rightarrow 2}\left[\frac{z^2-5 z+6}{z^2-4}\right]$

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Answer

$\lim _{x \rightarrow 2} \frac{z^2-5 z+6}{z^2-4}$
$=\lim _{x \rightarrow 2} \frac{(z-3)(z-2)}{(z+2)(z-2)}$
$=\lim _{x \rightarrow 2} \frac{z-3}{z+2} \quad \ldots\left[\begin{array}{l} \because z \rightarrow 2, z \neq 2, \\ \therefore z-2 \neq 0 \end{array}\right]$
$=\frac{\lim _{z \rightarrow 2}(z-3)}{\lim _{x \rightarrow 2}(z+2)}$
$=\frac{2-3}{2+2}$
$=-\frac{1}{4}$

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