RemaindersIntegral - Remainders for the Integral Test Study...

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Remainders for the Integral Test Study Guide When we first covered section 10.3, we skipped over the remainder estimate for the integral test. Since this may appear on the exam, we have decided to write up a short study guide on the topic. Note: The book also includes a lower bound for the remainder . In our opinion, this is unlikely to appear V 8 on the exam, so we did not include any problems on it. There is an explanation for the lower bound at the end of the summary (see pg. 602 of the text for an example calculation using the lower bound). Outline The basic formula is: V Ÿ 0 B .B 8 8 _ ( a b where is the remainder (i.e. ) for the series . V =  = 0 8 8 8 8œ" _ " a b A short summary concerning this estimate (including an explanation of this formula, two worked examples, and 10 practice problems) starts on the next page. After the summary are complete solutions to the 10 practice problems. Examples: Essential Problems: Other Problems: 1, 2 1, 3, 5, 7, 9 2, 4, 6, 8, 10 Answers to the Problems 1. 2. !Þ!# " " $!!! # ¸ ¸ !Þ!# "! ¸ !Þ" # "!! 0.0003 3. 4. a b a b ln tan # " 1 5. 6. 7. 8. 9. 10. , ' " '" / # ¸ !Þ!% ¸ !Þ!"( "!! ## !#( ln Œ
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Remainders for the Integral Test Summary The following picture illustrates the integral test for a convergent series: C B " # $ ' % C œ 0ÐBÑ ( ) * ! 0Ð"Ñ 0Ð#Ñ 0Ð$Ñ 0Ð%Ñ 0Ð'Ñ 0Ð(Ñ 0Ð)Ñ 0Ð*Ñ The area of the boxes is , and therefore: " a b 8œ" _ 0 8 " a b a b ( 8œ" _ ! _ 0 8 Ÿ
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RemaindersIntegral - Remainders for the Integral Test Study...

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