Question

How do you find the limit of `(abs(x^2-25))/(x+5)` as x approaches -5?

Answer 1

This limit does not exists.

Explanation:

`(abs(x^2-25))/(x+5) = (abs(x+5)abs(x-5))/(x+5) = "signum"(x+5)abs(x-5)`

We have two options

`lim_{x->-5^-}"signum"(x+5)abs(x-5) = -10` and
`lim_{x->-5^+}"signum"(x+5)abs(x-5) = 10` so this limit does not exists