Engineering Math I – Fall 2014
Quiz #7
Name:
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) = sin x. Which of the following is true?
(a) f is one-to-one.
(b) The function g = sin−1 x is the inverse of f for all x.
(c) f is one-to-one for − π2 ≤ x ≤
π
2
(d) f is one-to-one for 0 ≤ x ≤ π.
Problem 2 (4 pts). Suppose g is the inverse function of f and f (4) = 5, f 0 (4) = 32 . Find
g 0 (5).
(a)
2
3
(b)
9
5
(c)
3
2
(d) None of the above.
MATH 151:549-551 – Fall 2014
Quiz #7
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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 (5 pts). The geologist C. F. Richter defined the magnitude of an earthquake
to be log10 (I/S), where I is the intensity of the quake (measured by the amplitude
of a seismograph 100 km from the earthquake) and S is the intensity of a “standard”
earthquake (where the amplitude is only 1 micron = 10−4 cm). The 1989 Loma Prieta
earthquake that shook San Francisco had a magnitude of 7.1 on the Richter scale. The
1906 San Francisco earthquake was 16 times as intense. What was its magnitude on the
Richter scale?
MATH 151:549-551 – Fall 2014
Quiz #7
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The following problem had a typo when given in class, which has been corrected on this
version.
2
Problem 4 (7 pts). Let r(t) = h √tt+3 , ln(t2 − 1)i
(a) (2 pts) What is the domain of r(t)?
(b) (3 pts) Does the curve traced by r(t) in the Cartesian plane ever cross the x-axis?
What about the y-axis? Determine the quadrant(s) in which the curve lies.
(c) (2 pts) For which value(s) of t does r(t) = h4, ln 3i?