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.