epsilon delta criterion for continuous functions
Iīm given a rational function and fixed epsilon and x_0.
How do I find a delta to this epsilon in general?
Hereīs what I do:
I use |f(x)-f(x_0)|<epsilon and try to do some algebra till I get it in the form: |x-x_0|.A<epsilon
unfortunately A is in most if the cases dependent on x.
So how can I practically get rid of the x in A so that I can divide by A and set epsilon/A=delta ?
hereīs and example: f(x)=1/x
what do I do now? I tried using inequalities but it went all wrong, since I cannot use >=, cause I could thereby possibly get something greater than e, all thatīs left to me is using <= or..?
thanks for the help in advance!