Su09_Final_Exam-S.Curran

Su09_Final_Exam-S.Curran - Math 16A Summer 2009 Name Each...

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Math 16A, Summer 2009 Final Exam Name: Each Problem is worth 10 points. Problem 1 2 3 4 5 6 7 8 9 10 11 12 Total Score / 120 Problem 1. For each question below, circle True or False. DON’T GUESS , 2 points for each right answer, minus 2 points for each wrong answer. (a) True or False : Suppose that two cars are racing. After t seconds the first car is traveling at velocity v 1 ( t ) feet per second and the second car at v 2 ( t ) feet per second. If the average value of v 1 ( t ) on [0 , 60] is equal the average value of v 2 ( t ) on [0 , 60], then the cars have travelled the same distance after 60 seconds. (b) True or False : integraldisplay xe x dx = e x ( x - 1) + C. (c) True or False : y = 1 + e 2 x satisfies the differential equation y = 2 y. (d) True or False : d dx bracketleftbiggintegraldisplay x 1 2 ln t dt bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle x =1 = 0 . (e) True or False : As n gets very large, bracketleftbigg 1 n + 2 n + · · · + n - 1 n bracketrightbigg · 1 n approaches 1. (Hint: This is a Riemann sum.)
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Problem 2. Compute the following indefinite integrals: (a) integraldisplay 2 x - 3 dx (b) integraldisplay e 4+3 x dx
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Problem 3.
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