Proving Continuity of exp(x) at c=0

[skoomafiend]

Homework Statement

use delta, epsilon to prove that e^x is continuous at c = 0

Homework Equations

(a) for y>0, lim_n-> inf, y^(1/n) = 1
(b) for x < y, exp(x) < exp(y)

The Attempt at a Solution

im not sure how to approach this problem.
i have,
|exp(x) - exp(0)|= |exp(x) - 1|
so then exp(x) < 1 + ε
for δ > 0,
exp(δ) < 1 + ε

so then, i would set δ=ln(1+ε) for the proof?

also I am not sure how to use relevant eqn (a) to help with the problem. some insight would be appreciated. thank you.

 

[sunjin09]

You are not supposed to use log; you are supposed to use the two conditions (a) and (b); first you realize that the limit in (a) is fairly close to your limit, if you set y=e, then you can use that limit to come up with a delta which is a function of the N(epsilon) of that limit.