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I accept full responsibility under the Haverford Honor System for my conduct on this exam.
Math 113 Exam #1
October 1, 2010
Instructions: You are welcome to use one sheet of notes, but no other references or tools are allowed
(no textbooks, no calculators, etc.). This is a 55 minute exam; you may start working at 10:35 am
and must stop at 11:30 am. To receive full credit for a correct answer you must demonstrate how you
arrived at that answer. To receive partial credit for an incorrect answer your work must be clearly
explained. Please hand in your exam with the honor pledge signed.
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1. What are the domain and range of the function f (x) =
x
√e
?
x4 −1
2. Let f (x) = e3x−2 . Is f invertible? Why or why not? If f is invertible, what is f −1 (x)?
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3. For each of the following, either evaluate the limit or explain why it doesn’t exist.
(a)
√
4− x
lim
x→16 x − 16
(b)
lim √
x→−∞
3
6x2
7x4 + 9
(c)
x2 + x − 2
x→−2 x2 + 4x + 4
lim
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4. (a) At which numbers is the function h(x) = cos
(b) What is limx→0 h(x)? Explain your reasoning.
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x
1−x2
continuous? Justify your answer.
5. Suppose, for some bizarre reason, NASA built a giant landing platform at the level of the cloud tops
on Jupiter. If you’re standing on the platform and toss a ball straight up with an initial velocity of 32
m/s, its height (in meters) above the platform is given (approximately) by
s(t) = −13t2 + 32t.
Given that, what is the velocity of the ball 2 seconds after you release it?
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