Recent content by 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|...

I don't quite see why that would be true.

just one more question, when writing out the formal proof. how/where would i add the case for zero? since that case would need to have epsilon prime set to a different value. the other thing i was confused about was: i've been given an e' for a certain N' but for my proof i have set e' as some...

thank you for all your help. i think i have it now.

now do i say that for every ϵ > 0, there exists an N such that all n >= N where |\sqrt{a_n} - \sqrt{A}| < ϵ = \frac{ϵ'}{\sqrt{2}}

i'm definitely having trouble arranging the proof correctly. the given ϵ′ is for | a_n - A| < ϵ' ?

Since, |a_n - A| < ε We have that for, ε' > 0 there exists N such that for all n>=N, |\sqrt{a_n} - \sqrt{A}| < ε' so, |\sqrt{a_n} - \sqrt{A}| < ... < \frac{|a_n - A|}{\sqrt{A}} < \frac {ε'}{\sqrt{A}} = ε where ε' = ε\sqrt{A} I feel as though I'm missing some critical parts of the...

ε' = ε \sqrt{A} would this work? thank you for all your help so far.

i am trying to show that for all ε > 0, there is an N such that for all n>=N i'll have, |\sqrt{a_n} - \sqrt{A}| < ε i'm not understanding how to relate this (below) to my epsilon. |\sqrt{a_n} - \sqrt{A}| < \frac{|a_n - A|}{\sqrt{A}}

this is about where I'm getting stuck. would be able to rephrase that question in any other way?

bumping an old post, but i am having trouble with a similar problem. how would one continue from where he ended off? thanks!

Hey! I actually just got it. Thank you so much!

EDIT: this post was confusing. sorry! got it now though.

Do you mean solving for Ik+1 and then evaluating the integral between x=0 and x=1? i'm ending up with Ik+1 = 0

i still feel as if I am integrating in circles and i don't see the bigger picture. EDIT: just saw your most recent post. i'll try your suggestion. thanks!