math 172 sample papers - Math 172: Second Semester Calculus...

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Math 172: Second Semester Calculus Spring Semester, 2007 Final Exam Name: Section: ID Number: Instructions: Work must be shown to receive credit. No calculators. Question 1. (15 points) Solve the differential equation x y dx dy sin 2 subject to the initial condition 1 ) 0 ( y . # 1 2 3 4 5 6 SubTotal worth 15 20 15 15 20 15 100 score # 7 8 9 10 11 12 SubTotal Grand Total worth 15 15 20 15 15 20 100 200 score
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Question 2. (20 points) Find the volume of the solid obtained by rotating the region bounded by 1 , 0 , 0 ), 1 ( x x y x x y about the x-axis.
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Question 3. (5 points each) Evaluate the following integrals (A) 3 1 ) ln( dx x x (B) dx x x ) ( sec ) tan( 2 (C) dx x 2 / 3 2 ) 4 ( 1
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Question 4. (15 points) Determine whether the following integral is convergent or divergent. Evaluate it if convergent. 1 7 dx e x
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Question 5. (A) (10 points) Determine the interval of convergence (including behavior at endpoints) for 1 3 ) ( n n n n x x f .
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(B)
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math 172 sample papers - Math 172: Second Semester Calculus...

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