Question

Find the limit as x approaches positive infinity. \displaystyle\lim_{x\to\infty}\dfrac{\sqrt{9x^6+4x^2}}{x^3-1}

Answer 1

3

Explanation:

We are given that a function

`f(x)=(√(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)(√(9x^6+4x^2))/(x^3-1)`

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

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

Because
`(1)/(\infty)=0`

`\lim_(x\rightarrow\infty)(√(9x^6+4x^2))/(x^3-1)=3`

Answer: 3