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Unformatted text preview: Mat 315 Review for Exam 1 January 28, 2008 The first exam is Monday, February 4. The exam will cover sections 5.3, 5.4, 2.4, and 2.7. You should study your homework assignments, the notes for the class and the examples and proofs in the book. You definitely should know the definitions of the following terms: infinite series partial sum of an infinite series convergent or divergent series harmonic series geometric series absolutely convergent, conditionally convergent rearrangement Also know the following theorems: ( ) Rolle's Theorem Mean Value Theorem (MVT) ( ) Corollary 5.3.3: If g (x) = 0 for all x then g is constant L'Hospital's Rules (0/0 case and / case) Cauchy Condensation Test ( ) Algebraic Limit Theorem for Series ( ) Geometric Series Formula P-test Cauchy Criterion for Series nth Term Test for Divergence ( ) Comparison Test ( ) Absolute Convergence Test Alternating Series Test Theorem 2.7.10: Rearrangement of an absolutely convergent series The exam will have: One question that asks for statements of theorems or definitions One question that is very similar to homework problems One question that asks you to prove one of the starred theorems on the first page One question that asks you for examples Examples of series with particular properties from chapter 2. Examples of functions and their derivatives from chapter 5. One question that gives you some series and asks you to apply the tests to determine convergence (possibly absolute/conditional) Other questions The MVT is very important. ...
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- Winter '08