W2017 Math 267 Final Examination Solution.pdf

W2017 Math 267 Final Examination Solution.pdf - UNIVERSITY...

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Question Total Marks Actual Marks Part A 80 17 15 18 10 19 15 Total 120 UNIVERSITY OF CALGARY FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS AND STATISTICS FINAL EXAMINATION (SOLUTION) MATH 267 L01-L02 Winter 2017 DATE: 18 April 2017 Time: 3:30 pm – 6:30 pm Student ID Number: Last Name: First Name: Lecture Section EXAMINATION RULES 1. This is a closed book examination. 2. No calculators and no other aids are allowed for this examination 3. Answer Part A on the scantron sheet and Part B on the examination paper 4. Scantron sheets must be filled out during the exam time limit. No additional time will be granted to fill in scantron form. 5. The use of personal electronic or communication devices is prohibited. 6. A University of Calgary Student ID card is required to write the Final Examination and could be requested for midterm examinations. If adequate ID isn’t present the student must complete an Identification Form. 7. Students late in arriving will not be permitted after one-half hour of the examination time has passed. 8. No student will be permitted to leave the examination room during the first 30 minutes, nor during the last 15 minutes of the examination. Students must stop writing and hand in their exam immediately when time expires. 9. All inquiries and requests must be addressed to the exam supervisor. 10. Students are strictly cautioned against: a. communicating to other students; b. leaving answer papers exposed to view; c. attempting to read other students’ examination papers 11. During the final examination, if a student becomes ill or receives word of domestic affliction, the student must report to the Invigilator, hand in the unfinished paper and request that it be cancelled. If ill, the student must report immediately to a physician/counselor for a medical note to support a deferred examination application. 12. Once the examination has been handed in for marking, a student cannot request that the examination be cancelled. Retroactive withdrawals from the course will be denied. 13. Failure to comply with these regulations will result in rejection of the examination paper.
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Math 267 (L01-L02) - J. Ling, M. Pawliuk - Final Examination (Solution) - Winter 2017 2 PART (A) Multiple Choice Questions (80 marks) Instructions: On the scantron, fi ll in one answer per question. Each question is worth 5 marks. 1. Find the integral Z 5 cos ¡ 3 ¢  [Hint: Don’t use integration by parts 5 times.] (a) *** 1 3 ( 3 sin ( 3 ) + cos ( 3 )) + (b) 4 3 sin ( 3 ) 3 3 cos ( 3 ) + (c) 2 3 2 sin ( 3 ) + (d) 4 18 sin ( 3 ) + (e) 6 6 sin ( 3 ) + [Solution. We fi rst substitute = 3 We have  = 3 2  and so, Z 5 cos ¡ 3 ¢  = Z 3 cos ¡ 3 ¢ 2  = 1 3 Z cos   Next, we use integration by parts with = and  = cos   Then,  =  and we can use = sin  We have Z cos   = sin Z sin   = sin + cos +  Therefore, Z 5 cos ¡ 3 ¢  = 1 3 ¡ 3 sin ¡ 3 ¢ + cos ¡ 3 ¢¢ + 
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Math 267 (L01-L02) - J. Ling, M. Pawliuk - Final Examination (Solution) - Winter 2017
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  • Fall '15
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