Explore BrainMass

# Real analysis

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

We have just finished up integration and are done with a first course in analysis, chapters 1-6 of Rudin. We are also using the Ross and Morrey/Protter book.

Please answer question fully and clearly explaining every step. Any solution short of perfect is useless to me. So if you are not 100% sure whether your answer is right, then please do not answer.

The same problem is also attached as a word document with all the symbols.

******************************************************
Let f: [a,b] --> R an integrable function. Prove that:

i) lim *S* f(x) cos(nx) dx = 0

and

ii) lim *S* f(x) sin(nx) dx = 0.

where lim is n as it approaches plus infinity (it is
not specified so I believe the default when only n
is listed is to plus infinity, I may be mistaken),

*S* is my notation for the integral taken from a to b.