Real Analysis: continuity
Sorry, only a few more, lasts ones I'm not sure of, final on Friday, these are some of the review problems I don't get:
1) Show 2^x = 3x for some xE (0,1)
2) let f(x) = { x xrational
0 xirrational
a. prove lim f(x) = 0
x->0
b) Prove that lim f(x), does not exist for c not equal to 0.
x--> c
3) Suppose f is uniformly continuous on [a,b] and uniformly continuous on [b,c] Prove using an epsilon-delta argument that f is uniformly continuous on [a,c]
Thanks, this professor does a horrible job at teaching, and I'm really lost, any help, even how to start any of these would be great, thanks!