math_172_(fall_2008)_(schumaker)_final_exam_(spring08)

math_172_(fall_2008)_(schumaker)_final_exam_(spring08) -...

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Math 172: Second Semester Calculus Spring Semester, 2008 Final Exam Name: Section: ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. (10 points) Set up, but DO NOT EVALUATE, an integral for the arc length of the curve ) sin( x y , x 0 . # 1 2 3 4 5 6 SubTotal worth 10 18 18 16 18 20 100 score # 7 8 9 10 11 12 SubTotal Grand Total worth 20 20 15 15 15 15 100 200 score
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Question 2. Find the volume of the solid obtained by rotating the region bounded by y=0, x=0 and the line y= 2x+2 about the y axis. (a) (9 points) Use the method of cylindrical shells (integrate with respect to x) (b) (9 points) Use the method of cross-sections (integrate with respect to y) 0 1 2 1 2 3 x y
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Question 8. (20 points) Find the solution (assuming of the differential equation ), 2 ( y x dx dy that satisfies the initial condition 1 ) 1 ( y .
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(6 points each) Determine, with justification, whether each of the following series is absolutely convergent, conditionally convergent or divergent. (a)
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math_172_(fall_2008)_(schumaker)_final_exam_(spring08) -...

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