Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

oksuz_ Group TitleBest ResponseYou've already chosen the best response.0
show that the sequence of function given by \[fn(x)=nlog(1+\sin(x/n)) \] converges point wise to the identity function f(x)=x anyone has an idea ?
 5 months ago

BSwan Group TitleBest ResponseYou've already chosen the best response.0
like \(f_1(x)= log (1+sin x )\) \(f_2(x)=f_1+2 log (1+sin x/2 )\) ... ?!
 5 months ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
Use this: \(\sin x = x + O(x^3), \, x\rightarrow 0\). \[\lim_{n\rightarrow \infty}n\log\left(1 + \sin\left( x/n\right)\right) = \lim_{n\rightarrow \infty}\log\left(1 + x/n\right)^n\]
 5 months ago

BSwan Group TitleBest ResponseYou've already chosen the best response.0
it would be something like this : dw:1401617819184:dw
 5 months ago

oksuz_ Group TitleBest ResponseYou've already chosen the best response.0
@klimenkov at your solution last part equals e^x right? then when x goes to infinite e^x also goes to infinite.. should we consider identity function's interval here that is convergent ??
 5 months ago

klimenkov Group TitleBest ResponseYou've already chosen the best response.2
\(x\) is a fixed point and \(n\rightarrow \infty\). So it will converge for every finite \(x\). \[\log e^x = x.\]
 5 months ago

oksuz_ Group TitleBest ResponseYou've already chosen the best response.0
@klimenkov thank you..
 5 months ago

oksuz_ Group TitleBest ResponseYou've already chosen the best response.0
@BSwan thank you
 5 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.