My proof for this limit using the definition is correct? lim to 2^+ (1/(x-2)) = +\infty

My answer:

For all A > 0, exists \delta > 0 such that:
(1/(x-2)) > A so that 0 < x+2 < \delta.

Looking on inequality bellow between B, we have the key choose for \delta :

(1/(x-2)) > A
(x-2) < 1/A
x < 1/A+2

Like this, for \delta = 1/A+2, we have 1/(x-2) > A always that 0 < x-2 < delta.

1 Answer
May 31, 2018

See explanation

Explanation:

There is one mistake: 0 < x+2 < delta. After all, it is x-2 that you want to go towards 0.

I might also want to refine the wording a little, for instance:
"For all A > 0, there exists a delta>0 such that:" to make the proof clearer.

Also, as the proof presupposes that x>2, I might write:
2<x<2+1/A to make it clear that x lies between 2 and 2+1/A.

One other detail: You introduce B, but it's not clear where B belongs or what it refers to.