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