Question

How do you determine the limit of `(x+4)/(x-4)` as x approaches 4+?

Answer 1

`lim_(x->4^+) (x+4)/(x-4) = oo`

Explanation:

`lim_(x->4^+) (x+4) = 8`

`therefore 8lim_(x->4^+) 1/(x-4)`

As `lim_(x->4^+) (x-4) = 0` and all points on the approach from the right are greater than zero, we have:

`lim_(x->4^+) 1/(x-4) = oo`

`implies lim_(x->4^+) (x+4)/(x-4) = oo`