show that |(1/x)(1/(2+x)-.5)+(.25)| < epsilon if 0<|x| < delta, where delta is the smaller of the numbers 1, 4epsilon (epsilon being positive). translate this situation into a statement of the form [lim as x goes to X0 f(x)=A],specifying what you take for f, X0, and A.
my question is, what in the world is this asking? I know what the epsilon-delta limit definition is but what does this question want me to find? does it want me to find an epsilon and a delta or prove something about it?
It has found the delta for you. You need to prove the inequality for that value of delta, for every epsilon>0.
This is clearly an epsilon-delta proof, but for what function and what limiting value?
An $\epsilon-\delta$ proof asks you to show that, for any $\epsilon>0$, there is a $\delta>0$ for which $|f(x)-a|<\epsilon$ whenever $|x-x_0|<\delta$. Now what is $f(x)$, what is $x_0$, what is $a$? They gave you $\delta$, but you still need to prove the inequality for that $\delta$.