(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

(b) for x < y, exp(x) < exp(y)

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

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# Homework Help: Continuity of exp(x)

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