Question

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

Answer 1

`" limit" = 0`

Explanation:

`lim_(x->-oo) = (x^2+2)/(x^3+x^2-1)`

`lim_(x->-oo) = (1/x + 2/x^3)/(1 + 1/x-1/x^3)`

Putting `x = -oo`

`(1/(-oo) + 2/(-oo)^3 )/( 1 + 1/-oo - 1/(oo)^3 ) = 0/1 =0`

Therefore the expression approaches zero at negative infinity. graph{(x^2+2)/(x^3+x^2-1) [-10.25, 9.75, -5, 5]}