Engineering Math I – Fall 2014
Name:
Quiz #8
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). If g is the inverse function of f (x) = 2x + ln x, find g 0 (2).
(a) −2
(b) 3
(c)
5
2
(d) None of the above.
Problem 2 (4 pts). Find limx→∞ tan−1 (x2 ).
(a) 0
(b)
π
2
(c) − π2
(d) None of the above.
MATH 151:549-551 – Fall 2014
Quiz #8
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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). Let y = ln ln x.
(a) (2 pts) Find the domain of y.
(b) (2 pts) Find y 0 .
(c) (2 pt) Find an equation of the tangent line to y at the point (e, 0) .
MATH 151:549-551 – Fall 2014
Quiz #8
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Problem 4 (6 pts). A certain object cools at a rate (in ◦ C/min) equal to one-tenth of
the difference between its temperature and that of the surrounding air. If a room is kept
at 21◦ C and the temperature of the object is 33◦ C, find an expression for the temperature
of the object t minutes later.
MATH 151:549-551 – Fall 2014
Quiz #8
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Bonus Problem (2 pts). A curve passes through the point (0, 5) and has the property
that the slope of the curve at every point P is twice the y-coordinate of P . What is the
equation of the curve?