Question

Estimate the limit, if it exists.

Answer 1

0

Explanation:

The given limit is

`\lim_(x \to \infty) (x^2+x-22)/(4x^3- 13)`

Divide both the numerator and the denominator by the highest power of x in the denominator.

`=\lim_(x \to \infty) ((x^2)/(x^3)+(x)/(x^3)-(22)/(x^3))/((4x^3)/(x^3)- (13)/(x^3))`

This simplifies to;

`=\lim_(x \to \infty) ((1)/(x)+(1)/(x^2)-(22)/(x^3))/(4- (13)/(x^3))`

As
`x\to \infty, (c)/(x^n) \to 0`

`=\lim_(x \to \infty) (0+0-0)/(4- 0)=0`

The limit is zero