Evaluate the following limits : _ x -3 [x+3 x^2+4 x+3 ] - Vidyadip

Question

Evaluate the following limits : $\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$

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Answer

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

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