final_wi06 - Name: TA: Math 10B. Final Examination March...

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Name: PID: TA: Sec. No: Sec. Time: Math 10B. Final Examination March 21, 2006 Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. Write your solutions clearly and legibly. No credit will be given for illegible solutions. 1. (4 points) If f ( x ) is even and Z 3 - 3 { f ( x ) - 2 } dx = 6, Fnd Z 3 0 f ( x ) dx . # Points Score 1 4 2 8 3 10 4 6 5 8 6 8 7 8 8 6 Σ 58
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2. (8 points) Determine whether each improper integral converges or diverges; if it con- verges, Fnd its value. (a) Z 6 - 2 1 ( t + 2) 2 / 3 dt (b) Z 15 2 x ln( x ) dx
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3. A company earns revenue at a continuous annual rate of 0 . 04 (4%) of its net worth. At the same time, the company’s payroll obligations amount to 10 million dollars per year, paid out continuously. (a) (2 points) Write a diFerential equation that governs the net worth, W , of the company in millions of dollars. (b) (2 points) Determine the initial net worth
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final_wi06 - Name: TA: Math 10B. Final Examination March...

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