Evaluate the following one sided limits: _ x -2^+ x^2-1 2x+4 - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow-2^+}\frac{\text{x}^2-1}{2\text{x}+4}$

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Answer

$\lim\limits_{\text{x}\rightarrow-2^+}\frac{\text{x}^2-1}{2\text{x}+4}$
$=\lim\limits_{\text{x}\rightarrow2^+}\frac{(\text{x}-1)(\text{x}+1)}{2(\text{x}+2)}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{(-2+\text{h}-1)(-2+\text{h}+1)}{2(-2+\text{h}+2)}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{(-3+\text{h})(\text{h}-1)}{2\text{h}}$
$\Rightarrow\frac{-3\times-1}{2\times0}=\frac{1}{0}=\infty$

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