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Calculus II Problems - Fall2008_Prelim1

Calculus II Problems - Fall2008_Prelim1 - Sept 30 2008 Math...

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Sept. 30, 2008 Math 112, Prelim 1 Time: 7.30 - 9p.m. Instructions: 1) Write and your name your instructor's name on the front cover of the exam booklet. (Also put down your section number if you know it.) 2) Show all your work. A correct answer may get little credit unless it is clear that you use a correct method or give an adequate reason. 3) Do not simplify your answers unless required. 4) Do the problems in any order you like, but label the answers clearly. 5) This is a closed book test. Calculators, notes, or crib sheets are not allowed. There are some formulas on the back which may be useful. 1) (12 points) If , find . JÐBÑ B > .> J Ð Î# ( È ! B w # sin ± 2) (20 points) Sketch the region enclosed by the curves and , and find B #C B C " # the area of that region. 3) (20 points) Use the Trapezoid Approximaton with to estimate the integral . 8 % .B B ( " # (Do NOT simplify your answer.) Explain why this helps you to find an approximate value for 2. Use the following error bound formula, with the smallest possible value ln for
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