final_wi06 - Name TA Math 10B Final Examination Sec No PID...

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Name:PID:TA:Sec. No:Sec. Time:Math 10B.Final ExaminationMarch 21, 2006Read 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) Iff(x)is even andZ3-3{f(x)-2}dx= 6,findZ30f(x)dx.#PointsScore14283104658687886Σ58
2. (8 points) Determine whether each improper integral converges or diverges; if it con-verges, find its value.(a)Z6-21(t+ 2)2/3dt(b)Z2xln(x)dx15
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 peryear, paid out continuously.(a) (2 points) Write a differential equation that governs the net worth,W, of thecompany in millions of dollars.(b) (2 points) Determine the initial net worthW0that will keep the net worthconstant; in other words, determine the value ofW0for whichW=W0is an

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