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

Question

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

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Answer

$ \lim _{x \rightarrow-2}\left[\frac{-2 x-4}{x^3+2 x^2}\right]$
$=\lim _{x \rightarrow-2} \frac{-2(x+2)}{x^2(x+2)}$
$=\lim _{x \rightarrow-2} \frac{-2}{x^2} \quad \cdots\left[ \because x \rightarrow-2, x \neq-2,7$
$\therefore x+2 \neq 0 \right]$
$=\frac{\lim _{x \rightarrow-2}(-2)}{\lim _{x \rightarrow-2}\left(x^2\right)}$
$=\frac{(-2)}{(-2)^2}$
$=\frac{-2}{4}$
$=\frac{-1}{2} $

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