Real Analysis

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Power Series: Interval of Convergence

Find a power series for the function, centered at c, and determine the interval of convergence: f(x)= 4 / 5-x, c=-2

Limit comparison test

Use the limit comparison test to determine the convergence or divergence of the series En=1 2 / (3^n - 5)

Find the series summation

Find the series summation of the attached problem.

Extending power series.

Extend e^(x) into a power series at center x=1

Calculating the limits of a sequence.

Use two methods to calculate the limit of the following sequence. x(n)=1/n^3+2^2/n^3+...+n^2/n^3

What is 3/4 raised to the power of infinity?

Find the sum: infinity on top of the sigma sign, with i=1 under the sigma and 8(3/4)^(i-1) on the right hand side of the sigma.

Real Analysis on Integration 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.

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

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,

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,

Real Analysis Problem

We have learned Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class and we have finished differentiation. We just started integration. In this problem we are not supposed to use any material we haven't learned, ie integration. We are using the books by Rudin, Ross, Morrey/Protter. ****************************

Real analysis

Based on the Rolle, Lagrange, Fermat and Taylor Theorems. ****************************************************** Let f: [a,b] --> R, a < b, twice differentiable with the second derivative continuous such that f(a)=f(b)=0. Denote M = sup |f "(x)| where x is in [a,b] and g:[a,b] --> R, g(x)=(1/2)(x-a)(b-x) i) Prove

Proof of a limit point on a plane.

Prove that every infinite and bounded point collection in the plane (R2) has a limit point.