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Math 10C.
Midterm Exam 1
April 20, 2005
Turn off and put away your cell phone.
You may use a calculator, but no other electronic devices are allowed on this exam.
You may use one page of notes, but no books or other assistance on this exam.
Read each question carefully, answer each question completely, and show all of your work.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clarification.
1. (4 points)
g
is a function with continuous derivatives such that
g
(0) = 3,
g
0
(0) =

2,
and
g
00
(0) = 1.
(a) What is the Taylor polynomial of degree 2 for
g
centered at
x
= 0?
(b) The tangent line approximation for
g
(

0
.
1) is
g
(

0
.
1)
≈
3 + 0
.
2 = 3
.
2. Find a
better approximation for
g
(

0
.
1).
#
Score
1
2
3
4
Σ
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2. (6 points)
x
measures the time (in seconds) that you must wait at a certain traffic
signal for the red light to turn green. The probability density function for
x
is given
by
p
(
x
) =
(
1
40
if 0
≤
x
≤
40,
0
otherwise.
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 Spring '05
 Overholser
 Math, Normal Distribution, Probability theory, probability density function, Fundamental physics concepts, Cumulative distribution function, red light

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