Find the limit as x approaches positive infinity.

Ответ:

jessd18

08.01.2022

Step-by-step explanation:

We are given that a function

$f(x)=\frac{\sqrt{9x^6+4x^2}}{x^3-1}$

We have to find the value of given function when x approaches positive infinity.

$\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}\frac{\sqrt{9x^6+4x^2}}{x^3-1}$

$\lim_{x\rightarrow\infty}\frac{x^3\sqrt{9+\frac{4}{x}}}{x^3(1-\frac{1}{x^3})}$

$\lim_{x\rightarrow\infty}\frac{\sqrt{9+\frac{4}{x}}}{1-\frac{1}{x^3}}$

Because $\frac{1}{\infty}=0$

$\lim_{x\rightarrow\infty}\frac{\sqrt{9x^6+4x^2}}{x^3-1}=3$

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