M212_Final_Exam_Fall_2004

M212_Final_Exam_Fall_2004 - M212 Final Exam December 13,...

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Unformatted text preview: M212 Final Exam December 13, 2004 Name ID Signature Instructor Part A has 10 problems at two points each. No partial will be assigned here. Part B has 10 problems at 8 points each7 with partial credit to be given. DO Show all of your work here! Good Luck to Everyone! Part A Part B ' Page A1___ Page B1 Page A2_______ Page B2 Page A3________ Page B3 Page B4 TOTAL____________ Page B5 Page B6 Page B7 Page B8 Page B9 Page B10 TOTAL GRAND TOTAL PART A 2$~1 1—23. 1. (2pts) Find the inverse of the function f : 2. (2pts) Find the derivative of f = sec‘1(ex). 3. (2pts) Evaluate Sin(tan_1 2). Express the answer as a fraction. 4. (2pts) Write out the decomposition pattern for the 'nte a1 / 3m + 2 d2: 1 I" I -————-——— . g (x + 2)2(:z: + 3) (Do not compute the coefficients) A1 9. If i (or 6—1) is approximated by a T 4 summation, use alternating series to identify the upper error bound. 10. Judge the following series “AC”, “CC”, or “D”. .. °° —1 n 11). 2 (kn: A3 PART B 1. Use “parts” to integrate: / 2326"”“dx Answer_____—__(8pts) B1 2. Integrate: / Answer (8pts) B2 3. A “rectangular” swimming pool is 20 feet long, 12 feet wide, and 5 feet deep. If the water has a current depth of 4 feet, how much work would be required to pump all of the water out of the pool? (Use the fact that water weighs 62.5 lbs ./ft3). Answer______________(8pts) B3 00 1 4. Consider the series: Z 6(—§)"_1. 11:1 (2pts) Compute S. ii) On the grid below, plot S as a horizontal line, and illustrate an “6-strip” 0f %. (2pts) iii) Finally, plot the partial sums, 31, 52, 33, s4, s5, and 36 (4pts) B4 . . _ 0° (—1)"(:L’ — 1)” 5. Flnd the Interval of convergence for the serles: Z —————————. “:0 3”\/n + 1 (Be sure to check the endpoints)! Answer..- _ ____ (8pts) B5 {01“ . a: 6. Use power series techniques to evaluate / 0 1 + 11:3 Do leave your answer as a finite summation, but you must explain the error bound. dx with (E < .00005). (8pts) B6 7. a) State the “limit comparison test”. (4pts) b) Now demonstrate an application of this test with series that you choose! (4pts) B7 00 1 8. Confirm the convergence of the p-series Z 7 via the Integral Test. You must include TL 71:1 the appropriate conditions on f. (8pts) B8 9. a) Develop the Taylor series for f = 3—15, about a z 1. MW) 2 1 b) Use the above result to integrate / —da: and express 1n 2 as an infinite summation. 1 2: MW) B9 10. a) Develop the T2 polynomial for flat) 2 fl, about a : 25. Answer_______________ (4pts) b) Use the result above to compute the T2 approximation for V 27. Answer________________.__ (4pts) B10 ...
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This note was uploaded on 02/02/2010 for the course MATH-M 212 taught by Professor Grafpeters during the Spring '10 term at Indiana.

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M212_Final_Exam_Fall_2004 - M212 Final Exam December 13,...

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