Final2010guide.doc - Find its radius of convergence. 6....

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MATH 1B Sample Study Problems K Beal For 2010 FINAL EXAMINATION NOTE: Some topics on the final may not be here; some topics here may not appear on the final. Hopefully, the problems (of varying difficulty) will help you in creating your note sheet and will focus your studying. 1. Find the arc length of the graph of from to . Find the arc length of the graph of from to . 2. Use geometric series to express 0.0909090909090909… as the ratio of two integers. 3. Converge/Diverge? Remember to show your work to receive full credit. a. b. c. d. e. f. g. h. i. j. k. l. Absolutely Convergent/Conditionally Convergent/Divergent? a. b. 4. Find the interval of convergence of the power series . Let . Find the intervals of convergence for and . Find the radius of convergence of the power series 5. Find the Taylor series for the function centered at Find the Taylor series for the function centered at Find a power series representation for the function Find its radius of convergence. Find a power series representation for the function
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Unformatted text preview: Find its radius of convergence. 6. Solve the differential equation Solve the initial-value problem . 7. Consider the integral . Does this integral converge? If so, explain why and estimate the value to within 0.001. Find an interval centered about the origin within which can be approximated by with four decimal places of accuracy. Use a Taylor polynomial to approximate with an error of less than . Remember to explain why your approximation is within the specified error bound. 8. A detective finds a murder victim at 9am. The temperature of the body measured 90.3 . One hour later, the temperature of the body is 89.0 . The air-conditioned room has been maintained at a constant temperature of 68.0 a. Assuming the temperature, T, of the body obeys Newtons Law of Cooling, write a differential equation for T. b. Solve the differential equation found in (a) for T. c. Estimate the time the murder occurred, assuming the body was at 98.6 when the murder happened....
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This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at University of California, Berkeley.

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Final2010guide.doc - Find its radius of convergence. 6....

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