MATH267_F17_Final_exam_v11.pdf

# MATH267_F17_Final_exam_v11.pdf - Version 11 THE UNIVERSITY...

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Version 11 THE UNIVERSITY OF CALGARY DEPARTMENT OF MATHEMATICS AND STATISTICS FINAL EXAM MATH 267 L01 (Fall 2017) December 13, 2017 Time: 3 hours Fill out the following information as it appears on your Unicard. Example Your info FIRST NAME Alex LAST NAME Richardson I.D. NUMBER 19995790 NOTE: No calculators. No other aids. Closed-book. FOR TA USE ONLY Question Score MC /72 B1 /5 B2 /5 B3 /5 B4 /5 B5 /5 B6 /5 TOTAL /100 1

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Math 267 (L01) - M. Pawliuk - FINAL EXAM Version 11 - Fall 2017 2 PART (A) Multiple Choice Questions (72 marks) Instructions: On the scantron, fill in one answer per question. Each question is worth 4 marks. 1. (4 marks) Which of these is a sketch of the curve r = 1 2 + sin θ ? (A) 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 (B) 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 (C) 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 (D) 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 (E) 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 NOTE: The label A, B, C, D or E appears to the bottom left of the corre- sponding graph.
Math 267 (L01) - M. Pawliuk - FINAL EXAM Version 11 - Fall 2017 3 2. (4 marks) What is the slope of the tangent line of the curve r = θ 2 at θ = π 2 ? See diagram. 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 (a) 0, (b) - 1, (c) π 2 4 , (d) 2, (e) - 4 π . 3. (4 marks) What is the area of the region in that is inside both r = 1 and r = 1 + cos θ ? See diagram. 0 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 3 π 2 5 π 3 11 π 6 You may use the fact that R cos 2 θ dθ = 1 2 ( θ + sin θ cos θ ). (a) π + 3 π 4 - 2, (b) π 2 , (c) 0, (d) π , (e) π 2 + 3 π 4 - 2.

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Math 267 (L01) - M. Pawliuk - FINAL EXAM Version 11 - Fall 2017 4 4. (4 marks) A car travels along the path x ( t ) = 1 + 2 cos t y ( t ) = 3 + 2 sin t for 0 t 4 π . How far did it travel in total? (a) 2 π , (b) 4 π , (c) 8 π , (d) 16 π , (e) 32 π . 5. (4 marks) Consider the parametric curve C given by x ( t ) = 2 t + 1 y ( t ) = 1 1 + t 2 for -∞ < t < . What is the slope of the tangent line of C at t = - 1?
Math 267 (L01) - M. Pawliuk - FINAL EXAM Version 11 - Fall 2017 5

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