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Integration and Infinite Series

by: Kaylin Wehner

Integration and Infinite Series MATH 31B

Kaylin Wehner
GPA 3.55


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This 1 page Class Notes was uploaded by Kaylin Wehner on Friday September 4, 2015. The Class Notes belongs to MATH 31B at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 195 views. For similar materials see /class/177838/math-31b-university-of-california-los-angeles in Mathematics (M) at University of California - Los Angeles.


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Date Created: 09/04/15
Careful when applying LlHopitalls rule Ricardo Salazar Torres January 29 2009 Let us consider the following two examples where a little bit of thought could save us from disasteri li Compute the limit 12 sin I l i 1 111 I2 lt gt We might think that LlHopitalls rule is the perfect tool to attack this problem however notice that it gives zcosz2sinz lim 12 sin I DNE 12 xaoo 21 lim xaoo This limit does not exist because as 1 gets bigger the denominator tends to in nity but the term I cosz in the numerator oscillates between very large numbers and does not tend to any xed number At this point we might be tempted to conclude that the original limit 1 does not exist however if we use the sandwich theorem1 and the fact that 71 sinz S1 we get for z gt 0 271 S2s1nzlt2l z lt z2s1nz S Rhea zele 12 Therefore taking the limit as I A 00 we obtain 1 2 39 m 7g m um xaoo z xaoo z xaoo z 2 0S hm IltMgtSQ xaoo z Summarizing L Hopital s rule might lead us to think that the limit limgcnur00 Miti does not exist when it is actually equal to zero 1V J39hich you should remember from Math 31A


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