Evaluate the following limit: _ x 5 x^3-125 x^2-7x+10 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow5}\frac{\text{x}^3-125}{{\text{x}^2-7\text{x}+10}}$

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Answer

$\lim\limits_{\text{x}\rightarrow5}\frac{\text{x}^3-125}{{\text{x}^2-7\text{x}+10}}$
$=\lim\limits_{\text{x}\rightarrow5}\frac{(\text{x}-5)\big(\text{x}^2+25+5\text{x}\big)}{(\text{x}-2)(\text{x}-5)}$
$=\frac{(5)^2+25+5(5)}{(5-2)}$
$=\frac{25+25+25}{3}$
$=\frac{75}{3}=25$

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