A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
help!!
anonymous
 one year ago
help!!

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0show 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 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0like \(f_1(x)= log (1+sin x )\) \(f_2(x)=f_1+2 log (1+sin x/2 )\) ... ?!

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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it would be something like this : dw:1401617819184:dw

anonymous
 one year ago
Best 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 ??

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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@klimenkov thank you..
Ask your own question
Sign UpFind more explanations on OpenStudy
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.