Question

How do you find the limit of `1 / (x - 2)^2` as x approaches 2?

Answer 1

`lim_(x->2) 1/(x-2)^2 -> +oo`

Explanation:

Here we can see that as `x->2` from above and below `(x-2)^2 -> 0^+` (Because the term is squared)

Hence, `lim_(x->2) 1/(x-2)^2 -> +oo`

This maybe easier to visualise from the graph of `1/(x-2)^2` below.

graph{1/(x-2)^2 [-16.35, 15.68, -5.32, 10.69]}