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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:
  • Complicated
  • Convergence
  • Immediately
  • Differences
  • Definitions
  • Calculators
  • Partial Sums
  • General Formula
  • Approximations
  • Differentiate
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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 ? иии. It is strictly increasing if a1 < a2 < a3 < иии. 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,иии is increasing but not strictly increasing. {n2} = 1,4,9,16,иии is strictly increa...

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