# How I finish this proof using the definition of limit for this #lim_(x to 2) (-1/(x-2)^2) =-\infty #?

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#lim_(x to 2) (-1/(x-2)^2) =-\infty #

I wrote,

The limit exists #lim_(x to 2) (-1/(x-2)^2) =-\infty # if for all B < 0, exists a #\delta # , such that #-1/(x-2)^2# < B, always that 0 < |x-2| < #\delta # .

Looking for inequality we can choose the #\delta# more appropriate.

#-1/(x-2)^2 < B#

#-(x-2)^2 > 1/B#

I'm stuck here because I need the #\delta# positive. I don't know, how I complete this proof.

I wrote,

The limit exists

Looking for inequality we can choose the

I'm stuck here because I need the

##### 1 Answer

See below. You can always choose for instance

#### Explanation:

So if

As

So if

or

This can always be fulfilled, since you for any B can choose for instance

I hope this helps you on your way to solve your proof.