Question

How do you find `\lim _ { x \rightarrow - \infty } [ ( x - 2) ( x ^ { 2} - 1) ]`?

Answer 1

`-oo`

Explanation:

Expand brackets:

`(x-2)(x^2-1)= x^3-2x^2-x+2`

Since `x^3` changes more rapidly we only need to consider this in the limit to infinity:

`lim_(x->oo^-)x^3=-oo`