Engineering Math I – Fall 2014
Name:
Quiz #6
Section: 549 / 550 / 551
PART I: Multiple Choice. Read each problem carefully and work it out in the space
provided. Put a box around the answer you believe best answers the question. Calculators are not allowed.
√
Problem 1 (4 pts). Let f (x) = x2 − 3x. Find f 00 (4).
9
(a) − 32
(b)
27
32
(c)
4
3
(d) None of the above.
Problem 2 (4 pts). Suppose x2 + y 3 = 1. Find y 00 by implicit differentiation.
(a) y 00 = − 3y22
(b) y 00 =
4x−2y
3y 3
2x
(c) y 00 = − 3y
2
(d) None of the above.
MATH 151:549-551 – Fall 2014
Quiz #6
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PART II: Free response. Read each problem carefully and work it out in the space
provided. Circle your final answer.
Problem 3 (6 pts). Suppose the position of a particle is given by the vector function
r(t) = ht3 , t2 i.
(a) (2 pts) Sketch the curve traced by r(t) for −2 ≤ t ≤ 2. Indicate with arrows the
direction in which t is increasing.
(b) (3 pts) Find the velocity and acceleration of the particle when t = 2.
(c) (1 pt) Is the particle speeding up or slowing when t = −1? Explain your answer.
MATH 151:549-551 – Fall 2014
Quiz #6
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Problem 4 (4 pts). A satellite completes one orbit of Earth along the equator at an
altitude of 2000 km every 2 hours. Find the velocity of the satellite for any given time.
[Hint: Assume the satellite has a circular orbit and parametrize the orbit of the satellite.
Use the value 6600 km for the Earth’s radius; use hours as the unit for time.]
MATH 151:549-551 – Fall 2014
Quiz #6
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Bonus Problem (2 pts). At what point does the curve s(t) = ht(t2 − 3), 3(t2 − 3)i cross
itself? Find two unit vectors in the directions of both tangents at that point.