prove that by epsilon deltacant understand why he choose such x
we need to prove that their is so for every
their is x and
so we are free to choose our epsilon and our x
x cannot be equal to -1 because of the denominator.
and we need to choose x for which
but x=-1 there so we have a problem.
where is the problem in my way???
the prof solved it by
It's not true that you are totally free to choose any ε that you like.
As CaptainBlack told you, the actual limit is 2/3.
|1 - 2/3| = 1/3. So, if you use an ε ≥ 1/3, it is possible to find a δ > 0 such that for all x for which 0 < | x - 2 | < δ it follows that | x/(x+1) - 1 | < ε .
That's why CB said you need to choose ε < 1/3 .