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MATH 111
Exam I January 31, 2006
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Total 50
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GOOD LUCK!
- (18 points) The following is the graph of distance versus time for a moving object. Let D(t) represent the distance the object has traveled in feet after t seconds.
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0 5 10 15 20 25 30 35 40 45 50
distance (in feet)
time (in seconds)
(a) Find the object’s average trip speed after 25 seconds.
ANSWER: ats = feet per second (b) Compute the object’s average speed over the interval from t = 10 seconds to t = 35 sec- onds.
ANSWER: average speed = feet per second (c) Translate the following phrase into functional notation. the object’s average speed over the ten-second interval beginning at t seconds
ANSWER:
(d) Translate the following sentence into English: D(25 + h) − D(25) = 13. ANSWER:
(e) Find a ten-second interval over which the object travels exactly ten feet.
ANSWER: from t = to t = seconds
- (12 points) The graphs of f (x) and g(x) are given below.
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g(x)
f (x)
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(a) Find an interval of length 2 for which g(x + 1) − g(x) is negative, then 0, then positive.
ANSWER: from x = to x = (b) Find an x such that g(x) ≥ 4 and g(x) − f (x) = 4.
ANSWER: x =
(c) Find an x such that
f (x) x
g(x) x
ANSWER: x =
(d) Find an x such that f (x) − f (2) x − 2
ANSWER: x =
(e) List all values of x at whiche
g(x + 0.01) − g(x)
- 01
ANSWER: x =
