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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

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),0≤θ≤π.

(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),0≤θ≤π, in the xy-plane. Label the points from the

table above.

✲x

✻

y

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)