Evaluate the following limit: _ x 5x^3-6 9+4x^6 - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5\text{x}^3-6}{\sqrt{9+4\text{x}^6}}$

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Answer

$\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5\text{x}^3-6}{\sqrt{9+4\text{x}^6}}$$=\lim\limits_{\text{x}\rightarrow{\infty}}\frac{5-\frac{6}{\text{x}^3}}{\sqrt{\frac{9}{\text{x}^6}+\frac{4\text{x}^6}{\text{x}^6}}}$
$=\lim\limits_{\text{x}\rightarrow{\infty}}\frac{\Big(5-\frac{6}{\text{x}^3}\Big)}{\sqrt{\frac{9}{\text{x}^6}+4}}$
$=\frac{5}{\sqrt{4}}=\frac52$

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