# Lecture Notes for MATH 2300 - Analytic Geometry and Calculus 2 with Preston at Colorado (CU)

## Notes Information

 Material Type: Review Sheet Professor: Preston Class: MATH 2300 - Analytic Geometry and Calculus 2 Subject: Mathematics University: University of Colorado - Boulder Term: -- Keywords: ComplicatedConvergenceImmediatelyDifferencesDefinitionsCalculatorsPartial SumsGeneral FormulaApproximationsDifferentiate      ## Sample Document Text

Review Sheet for Third Exam Mathematics 2300 November 15, 2006 The exam will cover all of Chapter 10. No calculators of any kind will be allowed. Definitions to know: When we say know the definitions, this is a good indicator that you should know the defi- nitions. Remember how you did with the definition of the limit on the last exam? Not so great, huh? Do better this time. . Limit of a sequence: The sequence {an} converges to L if, for any ? > 0, there is an integer N such that |an ?L| < ? for every n ? N. Example: limn?? n2+1n2 = 1 since for any ? > 0, we can choose N to be the first integer above 1??. Then if n ? N, we will have |an ?L| = | 1n2| < ?. . (Strictly) increasing: The sequence {an} is increasing if a1 ? a2 ? a3 ? ���. It is strictly increasing if a1 < a2 < a3 < ���. It is eventually increasing if deleting finitely many terms makes it an increasing sequence. Examples: {2n+(?1)n} = 1,3,3,5,5,7,7,��� is increasing but not strictly increasing. {n2} = 1,4,9,16,��� is strictly increa...

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