I am doing these practice problems to study for a test and I just can't figure them out, it's kind of frustrating. The first concerns the delta-epsilon proof. f(x) = 2-(1/x) x is approaching 1, and the limit is 1. Epsilon is given at 0.1 so, what I have... 0<|x-1|<d (delta) |f(x)-1|<.1 so |2-(1/x)-1|<.1 |1-(1/x)|<.1 Maybe I am just an idiot, but how do I go from there? The answer is delta=1/11, I just can't see how to get it... I mean, I have done other problems like it, like for lim x->3 (2x-5) L=1 e=.01 |2x-5-1|<.01 2|x-3|<.01 |x-3|<.005 so delta=.005 And this other problem: find the limit, using algebra, for x->0 of sin7x/sin9x I multiplied both sides by csc9x, to get (sin7x*csc9x)/1 because sinx*cscx=1, sin9x*csc9x=1 But I can figure out where to go from there. Am I doing it wrong? Thank you for any help!