Evaluate the following limits in Exercise: _ x -2 1 x +1 2 x+2 - Vidyadip

Question

Evaluate the following limits in Exercise:$\lim\limits_{\text{x}\rightarrow-2}\frac{\frac{1}{\text{x}}+\frac{1}{2}}{\text{x}+2}$

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Answer

$\lim\limits_{\text{x}\rightarrow-2}\frac{\frac{1}{\text{x}}+\frac{1}{2}}{\text{x}+2}$At x = –2, the value of the given function takes the form ${\frac{0}{0}}$.
$\text{Now},$$\lim\limits_{\text{x}\rightarrow-2}\frac{\frac{1}{\text{x}}+\frac{1}{2}}{\text{x}+2}$$=\lim\limits_{\text{x}\rightarrow-2}\frac{\Big(\frac{2+\text{x}}{2\text{x}}\Big)}{\text{x}+2}$
$\lim\limits_{\text{x}\rightarrow-2}\frac{1}{2\text{x}}$
$\frac{1}{2(-2)}$
$=\frac{-1}{4}$

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