Question

What is `limx->3` of `(2(x-3))/(|x-3|)`?

Answer 1

The limit does not exist.

Explanation:

`f(x) = (2(x-3))/abs(x-3) = {(2,"if",x > 3),(-2,"if",x < 3):}`

The one-sided limits are distinct, so the two-sided limit does not exist.