Final spring 2012

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15 Feb 2019
Department
Course
Professor
Northwestern University NetID:
ID #:
Math 230 Final Exam
Spring Quarter 2012
Tuesday, June 5, 2012
Instructions: Show ALL of your work on the pages provided! Explain your reasoning using
complete sentences and correct grammar, spelling, and punctuation. All numerical answers MUST
be exact; e.g., you should write πinstead of 3.14...,2 instead of 1.414..., and 1
3instead of 0.3333...
Make sure that your final answer is clearly indicated. This test has seventeen pages. Check to make
sure you have pages 1 - 17. Calculators, course notes, textbooks, etc. are NOT allowed. You have
120 minutes. Simplify your answers.
Do not write your name on this exam.
Write your NetID and your Student ID Number in the spaces provided at
the top of this page.
Mark your section!
Time Instructor
9:00 Li
10:00 Ridenour
11:00 Bode
12:00 Khorami
1:00 Wolf
2:00 Khorami
Question Points Score Question Points Score
1 13 8 16
2 8 9 20
3 10 10 12
4 19 11 14
5 14 12 17
6 10 13 17
7 10 14 20
Total 200
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Math 230 Final Exam Spring Quarter 2012 Page 2 of 17
Question 1. Consider the polar curve given by the equation r= 2 cos(2θ),0θπ.
(a) (5 points) Fill in the values of rin the table below.
θ r = 2 cos(2θ)
0
π
4
π
2
3π
4
π
(b) (8 points) Sketch the curve r= 2 cos(2θ),0θπ, in the xy-plane. Label the points from the
table above.
x
y
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Math 230 Final Exam Spring Quarter 2012 Page 3 of 17
Question 2. Sheldon is on a hiking trip with his roommate Leonard. Suppose that the gradient of
the temperature at their current location is pointing in the northwest (NW) direction. Answer each
of the following questions.
Hint: There might be more than one correct answer. Circle all correct answers!
(a) (4 points) Sheldon does not tolerate temperature changes. In which direction(s) could Sheldon
walk to avoid a change in temperature?
Northeast (NE) Northwest (NW) Southeast (SE) Southwest (SW)
(b) (4 points) Sheldon’s roommate Leonard, on the other hand, prefers lower temperatures. In which
direction(s) should Leonard walk in order to experience the largest decrease in temperature?
Northeast (NE) Northwest (NW) Southeast (SE) Southwest (SW)
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