# What is the limit as x approaches -2 from the right of the following equation?

## limit of f(x) as x approaches -2 from the right of $\frac{x + 2}{2 {x}^{2} + 5 x + 2}$

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Feb 6, 2018

$- \frac{1}{3}$.

#### Explanation:

Note that, $\frac{x + 2}{2 {x}^{2} + 5 x + 2} = \frac{x + 2}{\left(x + 2\right) \left(2 x + 1\right)}$.

$\therefore \frac{x + 2}{2 {x}^{2} + 5 x + 2} = \frac{1}{2 x + 1} , \mathmr{if} x \ne - 2$.

Now, as $x \to - 2 + , x > - 2 , \text{ hence, } x \ne - 2$.

$\therefore {\lim}_{x \to - 2 +} \frac{x + 2}{2 {x}^{2} + 5 x + 2}$,

$= {\lim}_{x \to - 2 +} \frac{1}{2 x + 1}$,

$= \frac{1}{2 \left(- 2\right) + 1}$.

$\Rightarrow {\lim}_{x \to - 2 +} \frac{x + 2}{2 {x}^{2} + 5 x + 2} = - \frac{1}{3}$.

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