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Lecture Notes for MAC 2312 - Calculus II with Rosenthal at Florida International (FIU)

Notes Information

Material Type:Class Note
Professor:Rosenthal
Class:MAC 2312 - Calculus II
Subject:Mathematics Calculus and Precalculus
University:Florida International University
Term:--
Keywords:
  • Either...or
  • Exponential
  • Closed Form
  • Convergence
  • Absolutely Convergent
  • Conditionally Convergent
  • Telescoping
  • Taylor Series
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Is ?u k geometric? START Is ?u k telescoping? Does ?u k have all positive terms? Does ?u k contain factorials &/or exponential functions? Is 0lim ? ?? kk u ? Is ?u k alternating? Converges is -1< r < 1 Diverges if 1??r or 1?r Write Sn in closed form. Converges if n n S ?? lim exists. Diverges if n n S ?? lim d n.e. Is ?u k a p-series? Let f(x) be the function that results when k is replaced by x in the formula for ku . Is f decreasing and continuous for 1?x , and do you know ( )? dxxf ? Converges if p >1. Diverges if 10 ?< p Use ratio test. Converges if 1lim 1 <+ ?? k k k u u Diverges if 1lim 1 >+ ?? k k k u u ( ) ?+or Diverges by divergence test Use integral test. If integral conv...
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