MTH 201 Final, Fall 2012

Lebanese American University – Byblos Fall 2012 Calculus III – Final Exam Date: 25/01/2013 Name : Duration: 2h 15 1. (5 points) Evaluate the integral 2. (20 points) Study the convergence of these improper integrals without calculating them, then find their values when they converge: a. b. 3. (6 points) Determine if the series converges or not. 4. (20 points) Determine if each of the following series are absolutely convergent, conditionally convergent or divergent. a. b. c. 5. (10 points) Find the interval of convergence and the radius of convergence of the power series 6. (9 points) Use Maclaurin series to estimate with an error of magnitude less than 7. (10 points) Let Determine if the limit of as exists or not. 8. (10 points) Find the volume under the parabolic cylinder whose base is the region enclosed by the parabola and the line in the -plane. 9. (8 points) Find the double integral 2 6 x y   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - x y  6 10. (12 points) Find the double integral where is the region inside the circle satisfying and