Answer:
3
Step-by-step explanation:
We are given that a function
[tex]f(x)=\frac{\sqrt{9x^6+4x^2}}{x^3-1}[/tex]
We have to find the value of given function when x approaches positive infinity.
[tex]\lim_{x\rightarrow\infty}f(x)=\lim_{x\rightarrow\infty}\frac{\sqrt{9x^6+4x^2}}{x^3-1}[/tex]
[tex]\lim_{x\rightarrow\infty}\frac{x^3\sqrt{9+\frac{4}{x}}}{x^3(1-\frac{1}{x^3})}[/tex]
[tex]\lim_{x\rightarrow\infty}\frac{\sqrt{9+\frac{4}{x}}}{1-\frac{1}{x^3}}[/tex]
Because [tex]\frac{1}{\infty}=0[/tex]
[tex]\lim_{x\rightarrow\infty}\frac{\sqrt{9x^6+4x^2}}{x^3-1}=3[/tex]
Answer: 3
