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August 31st, 2010, 02:06 PM  #1 
Newbie Joined: Aug 2010 Posts: 1 Thanks: 0  Question regarding uniform convergence
Hello, I have a question as follows: Let f_n(x) = 1 + sin(x/n) + x/n Does the sequence *{f_n}n=1 to n=inf* converge pointwise on **[0,inf)**? If it does, what is the limit function? Does the sequence * converge uniformly on **? Does it converge uniformly on [0,1]? OK I've found that the sequence does indeed converge pointwise to f(x) = 1, and that it does not converge uniformly on **. I am however, struggling to work out if it converges uniformly on [0,1], Any help is appreciated, Thank you. 
September 1st, 2010, 01:37 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,586 Thanks: 612  Re: Question regarding uniform convergence
The slowest convergence in the interval [0,1] is at x=1, so uniformity is shown by convergence at all x using the ? ? for x=1.


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convergence, question, uniform 
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