Monthly Archives: April 2011

September 2001 #2

Problem Statement: Suppose that converges absolutely. Prove that converges for every . Proof: We are given that  converges absolutely, this implies that  converges. By definition this means that the sequence of partial sums, , converges. But every convergent sequence is also Cauchy. Let … Continue reading

Posted in Analysis, Cauchy, Sequence, Series | Tagged , , | 3 Comments

September 2001 #1

Problem Statement: Let be differentiable on and suppose that exists and is finite. Prove if exists and is finite, then . Proof: Suppose that and that . Since these limits exist we know that these limits will exist, and be the … Continue reading

Posted in Analysis, Cauchy, Continuity, Differentiable, Math, MVT, Sequence | Tagged , , | Leave a comment

Winter 2004 #4

Problem Statement: Suppose that is differentiable on the bounded interval . Suppose further that there is a constant such that for every . Show that exists and is finite. Note: When I read this question the first time I thought the … Continue reading

Posted in Analysis, Cauchy, Continuity, Differentiable, Math, MVT, Sequence, Uniform Continuity | Tagged , , | 4 Comments

Welcome!

Hi! My name is Erin and I’m a grad student at Cal Poly getting my M.S. in Mathematics. Currently my days are filled with teaching and studying, which brings us to this blog. In 38 days I have to take … Continue reading

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