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August 31st, 2010, 03:06 PM   #1
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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.
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September 1st, 2010, 02:37 PM   #2
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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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