APPM1360Spring07Test1

APPM1360Spring07Test1 - Exam#1 APPM 1360 Spring 2007 ON THE...

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Exam #1 APPM 1360 Spring 2007 ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture section (4) your instructor’s name, and (5) a grading table. You must work all of the problems on the exam. Show ALL of your work in your bluebook and box in your final answer. A correct answer with no relevant work may receive no credit, while an incorrect answer accompanied by some correct work may receive partial credit. Text books, class notes and calculators are NOT permitted. 1. ( 24 points, 8 each ) Integrate the following: (a) Z tanh x ln ( cosh x ) d x , (b) Z 2 1 x + 2 x 2 + x d x , (c) Z ( 5 - 3 x ) e 2 x d x 2. ( 16 points, 8 each ) Consider the following di ff erential equation and initial condition: cosh x d y d x + sinh x y = e - x , y ( 0 ) = 0 (a) Solve the equation with this initial condition. (b) Verify your solution by directly substituting it to the equation. 3. ( 30 points, 10 each ) A bowl is constructed by rotating the region in the first quadrant enclosed by the functions y = x 2 / 2 and y = h around the y –axis (see the figure). (a) Using disk–washers find the volume of the bowl. How high should the bowl be if its total volume is 16
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