help on proving limit questions.

[serenaleesl]

Prove that lim(x->2) (1/x)= 1/2.?
why is the delta set at (1,2*epsilon)..i thought it's supposed to be (1,6*epsilon)?the steps are as follows:-
|1/x - 1/2| = |x-2|*1/2|x|
=1/2|x-2| (why do they eliminate x in this step?)
<1/2 delta
= epsilon..
i dont understand..

 

[pka]

The 1/|x| was not dropped is was replaced by 1.
\(\displaystyle \left|{x-2}\right|<\delta\leqslant1\,\Rightarrow\,1<x\,\Rightarrow\,\frac{1}{\left|x\right|}}<1\)