Question

What is the limit of `(-5x^3) /( 3x^2-1)` as x approaches infinity?

Answer 1

`= - oo`

Explanation:

`lim_{x to oo} (-5x^3) /( 3x^2-1)`

`=lim_{x to oo} -x * (5) /( 3-1/x^2)`

`= lim_{x to oo} -x * lim_{x to oo} (5) /( 3-1/x^2)` (as both these limits exist)

`= - oo * (5) / 3`

`= - oo`