Question

How do you evaluate the limit of `(x^2-16)/(x+4)` as `x->-4`?

Answer 1

`-8.`

Explanation:

`lim_(x to -4) (x^2-16)/(x+4),`

`=lim_(x to -4) {(x+4)(x-4)}/(x+4),`

`=lim_(x to -4) (x-4),`

`=-4-4,`

`:." The Reqd. Lim.="-8.`

Answer 2

`-8`

Explanation:

Start by factorising numerator/denominator.

`rArr(x^2-16)/(x+4)`

`=(cancel((x+4))(x-4))/(cancel((x+4)))=x-4`

`rArrlim_(xto-4)(x^2-16)/(x+4)`

`=lim_(xto-4)(x-4)`

`=-4-4=-8`