Question

How do you evaluate the limit of `lim (x^3+8)/(x^2-4)` as `x->-2`?

Answer 1

`-3`.

Explanation:

`"The Rqd. Lim.="lim_(x to -2) (x^3+8)/(x^2-4)`

`=lim_(x to -2) {(cancel(x+2))(x^2-2x+4)}/{(cancel(x+2))(x-2)}`

`=lim_(x to -2)(x^2-2x+4)/(x-2)`

`={(-2)^2-2(-2)+4}/(-2-2)`

`=12/-4`

`=-3`.