Question

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

Answer 1

`= oo`

Explanation:

let's say that this amounts to setting `x = 2 + epsilon qquad color{red}{epsilon > 0}`

so we have

`lim_{x to 2^{+}} 1/(x-2) = lim_{epsilon to 0} 1/(2 + epsilon - 2) = lim_{epsilon to 0} 1/epsilon`

because of the statement in red above, this term is positive and so `1/epsilon to + oo` as `epsilon to 0`

so

`lim_{x to 2^{+}} 1/(x-2) = oo`