Evaluate the following one sided limits: _ x -8^+ 2x x+8 . - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow-8^+}\frac{2\text{x}}{\text{x}+8}.$

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Answer

$\lim\limits_{\text{x}\rightarrow-8^+}\frac{2\text{x}}{\text{x}+8}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{2(-8+\text{h})}{(-8+\text{h)+8}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{-16+2\text{h}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{-16}{\text{h}}+2$
$\Rightarrow\frac{-16}{0}+2=-\infty$

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