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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