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Real Analysis

Functions: Limits

Using the definition of a limit (rather than the limit theorems) prove that lim {x -> a+} f(x) exists and find the limit in each of the following cases a) f(x) = x/|x|, a = 0. b) f(x) = x + |x|, a = -1. c) f(x) = (x - 1)/(x^2 - 1), a = 1. In which cases do lim {x -> a-} f(x) and lim {x -> a} f(

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.

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 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. ****************************