Evaluate the following limit: _ x 2 x^4-16 x -2 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$

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Answer

$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^4-16}{{\text{x}}-2}$
$=\lim\limits_{\text{x}\rightarrow2}\frac{\big(\text{x}^2+4\big)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$
$=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)(\text{x}+2)\big(\text{x}^2+4\big)}{({\text{x}}-2)}$
$=\lim\limits_{\text{x}\rightarrow2}{(\text{x}+2)\big(\text{x}^2+4\big)}$
$=(2+2)(4+4)$
$=4(8)$
$=32$

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