# Spring2012.pdf - UNIVERSITY OF WATERLOO FINAL EXAMINATION...

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UNIVERSITY OF WATERLOO FINAL EXAMINATION SPRING TERM 2012 Student Name (Print Legibly) Signature Student ID Number COURSE NUMBER MATH 118 COURSE TITLE Calculus 2 for Engineering COURSE SECTION(s) 001 002 003 004 DATE OF EXAM Tuesday August 7, 2012 TIME PERIOD 4:00p.m. - 6:30p.m. DURATION OF EXAM 2.5 hours NUMBER OF EXAM PAGES 11 INSTRUCTORS (indicate your section) Section 1: Chemical A. Chow Section 2: Geo/Env E. Dupont Section 3: Mechanical E. Dupont Section 4: Mechatronics A. Shum Supplementary EXAM TYPE Closed Book PAGE FORMAT Single sided ADDITIONAL MATERIALS No additional materials allowed Notes: 1. Fill in your name, ID number and sign the paper. 2. Answer all questions in the space provided. Continue on the back of the preceding page if necessary. Show ALL your work. 3. Check that the examination has 11 pages. 4. Your grade will be in- fluenced by how clearly you express your ideas, and how well you organize your solutions. Marking Scheme: Question Mark Out of 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 Total 80
MATH 118 - Final Exam. Spring Term 2012 Page 2 of 11 1. Determine if the following converge or diverge and state your reason why. (a) X n =1 5 4 n  (b) X n =1 e 1 n n  (c) X n =2 ( - 1) n n 1 2  (d) X n =1 [ln(1 + 1 n )] n  (e) X n =1 n n n !2 n 
MATH 118 - Final Exam. Spring Term 2012 Page 3 of 11 2. (a) Show that 2 x 1 + x 4 = X n =0 2( - 1) n x 4 n +1 and state the radius of convergence.  (b) Find a series representation of Z x 0 2 t 1 + t 4 dt and compute the interval of convergence.  (c) Find the sum of the series 2 3 X n =0 ( - 1) n 3 n (4 n + 2) 
MATH 118 - Final Exam. Spring Term 2012 Page 4 of 11 3. Let f ( x ) = 5 + x .
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