Question

X +4
2 - 16
lim
X→-4 X

Answer 1

I'm going to assume you meant to say

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

Factorize the denominator to reveal a removable discontinuity in the limand:

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

In the limit, we're considering values of x *near* -4, and not x = -4 itself. So we can cancel the factors of x + 4 and we're left with

`\displaystyle \lim_(x\to-4) (x+4)/(x^2-16) = \lim_(x\to-4) \frac1{x-4} = \frac1{-4-4} = \boxed{-\frac18}`