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

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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# .

My answer:

For all A > 0, exists

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

Like this, for

##### 1 Answer

See explanation

#### Explanation:

There is one mistake:

I might also want to refine the wording a little, for instance:

"For all A > 0, there exists a

Also, as the proof presupposes that

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