Proving Existence of lim (x--->c) {f(x)} = l

[maximus101]

suppose that f : (a,b)\{c} ----> real numbers is a function such that

lim (x--->c+) {f(x)} and lim (x--->c-) {f(x)} both exist and are equal to a common value l.

how can we actually prove that lim (x--->c) {f(x)} exists and that it equals l?

 

[micromass]

Try a \epsilon,\delta proof. It's not to hard if you do just that...