Evaluate the following limit: _ x4 x^2-16 x -2 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{4}}\frac{\text{x}^2-16}{\sqrt{\text{x}}-2}$

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Answer

$\lim\limits_{\text{x}\rightarrow{4}}\frac{\text{x}^2-16}{\sqrt{\text{x}}-2}$
$=\lim\limits_{\text{x}\rightarrow{4}}\frac{(\text{x}-4)(\text{x}+4)}{\big(\sqrt{\text{x}}-2\big)}$
$=\lim\limits_{\text{x}\rightarrow{4}}\frac{\big(\sqrt{\text{x}}-2\big)\big(\sqrt{\text{x}}+2\big)(\text{x}+4)}{\big(\sqrt{\text{x}}-2\big)}$
$=\lim\limits_{\text{x}\rightarrow4}{\Big(\sqrt{\text{x}}+2\Big)}{(\text{x}+4)}$
$=(2+2)(4+4)$
$=4(8)$
$=32$

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