Real Analysis Problem

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 specifi... click for more

Real Analysis Problem

We have just finished up integration and are done with a first course in analysis, so 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 believ... click for more

Real Analysis Problem

I need a correct and concise solution. The Problem: f : R --> R , f ' ' ' ' continous. Prove: S (from a to b) f (t) dt = [(b - a) / 6] ( f(a) + f(b) + 4 f( (a+b) / 2) ) for all a, b in R. f ' ' ' ' means four times differentiable. S means the integral

Real Analysis Problem

I need a correct and concise solution. If the answer is not 100% correct, I will ask for my money back! We just finished integration and are done with a first course in analysis, i.e. chapters 1-6 of Rudin. We are also using the Ross and the Morrey/Protter book. The Problem: f : R --> R , f ' ' ' ' continous. FIND ALL FUNCTIONS THAT SATISFY THE FOLLOWING: S (from a to b) f (t) dt = [(b - a) / 6] ( f(a) + f(b) + 4 f( (a+b) / 2) ) for all a, b in R. f ' ' ' ' means four times differentiable. S means the integral

Completing the square: Finding the vertex and intercepts - repel, attract or are indifferent?

Rewrite the function f(x)=x^2+13/3 x+7/3 in the form f(x)=(x+13/6)^2+ c Then need to find the vertex of parabola as the graph of f, finding the y and x intercepts. Find the fixed points of f state whether they repel, attract or are indifferent. Using a gradient, find the interval of attraction for one of the fixed points.