
DeltaEpsilon proof
I am having a real tough time with these proofs.
f(x)=2(1/x)
find delta such that 0<x1<d then f(x)1<0.1
I understand what it means, but I'm having a hard time proving it.
I start out by working the epsilon inequality...
I end up with something like this...
1/xx1<0.1
Now I'm stuck. But from what I've been reading you would set
x1<1
This is obviously not a good option given 1/x. So I chose 1/2.
I eventually get...
1/2<x<3/2
Now I don't understand the next step. This should be so easy.

Let $\displaystyle \delta = .05$ and $\displaystyle \left {x  1} \right < \delta < \frac{1}{2}$.
From what you have already done this means that $\displaystyle \frac{1}{x} < 2$.
Thus $\displaystyle \left {1  \frac{1}
{x}} \right = \left {\frac{{x  1}}
{x}} \right < 2\left {x  1} \right < 2\left( \delta \right) = 0.1$