Math 1320.001 Exam 01
Fall 2015
Name
SOL(Lh0
Student ID Number:
9orm 1
Class Number:__________
Instructions:
• Please remove headphones and hats during the exani
• The scheduled time for this exam is 8:35am 9:25am. You will be given
an additional 5 mm to finalize your solutions. Your exam must be sub
mitted promptly at 9:30am.
-
• Before beginning, read through the exam. It is recommended that you
begin with the problems you are most confident about solving.
• I will not answer questions during the exam. If you believe there is
a typo in the exam make a note on the problem and do your best to
demonstrate your understanding of the ideas being tested.
• Show all work, as partial credit will be given where appropriate. If no
work is shown, you may receive a score of zero for the problem.
• All final answers should be written in the space provided on the exam
and in simplified forum unless noted otherwise.
• CALCULATORS ARE NOT ALLOWED ON THIS EXAM
• This is a “closed notes/closed book’ exam You are not allowed any
outside aids during this exam. If you have papers at your desk during
the exam you will be given a zero on the exam.
-
• If your phone is out during the exam it will be considered a
cheating offense put your phone away!
-
IVlatlil32O.001
Exam 01, Page 2 of 11
For Grader Use Only
Question
Points
1
11
2
10
3
15
4
12
5
12
6
15
7
10
8
15
Bonus
0
Total:
100
Score
25 September 2015
Exam 01, Page 3 of 11
Mathl32O.001
2.5 September 201.5
WRITE YOUR ANSWERS IN THE PROVIDED BOXES
SHOW YOUR WORK
[11 pointsj
1. Arc Length.Fiiid the exact length of the curve defined by:
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for 0 <x < 8.
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3/2.
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3
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[10 points]
Exam 01, Page 4 of 11
25 September 2015
2. Average Value of a Function. Given
f(x)
find the
average
=
(a)cos(i)
3
—siri
value of f on the interval [0,
Pro&€tO1
ir].
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a
U -Sin(X)
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l\Iath1 320.001
[12 points]
Exam 01, Page 6 of 11
25 September 2015
4. Area Betweeu Curves. Find the area enclosed between the parabola y
2
the line y 2x. A graph of these curves has been provided.
=
16x and
Ir-CLaAA
LL r
<
2
WtTi.l’CSLCif
(OO)
(a) Begin by labeling each of the curves with the corresponding function.
(b) Next label the graph with the coordinates of the intersection points. [Show your
calculations.]
r
4x11
,4x24Loxo
J
4 (x- 4) o
)4
(c) Next sketch an approximating rectangle onto the graph of the region in preparation
for calculating the area of the enclosed region.
(d) Finally, set up the integral for calculating the area between the curves but do not
integrate. The integral is your solution.
d
r*Ca.€ 1-CCI€-L4
4J
0
hn -
=
4 (i-;;: -2x) dx
Jo
&I’L4
j’ft
-
0
IVlathl32O.001
[12 points]
Exam 01, Page 7 of 11
25 September 2015
5. Population Growth. A bacteria culture initially contains 100 cells and grows at a rate
proportional to it’s size. After an hour the population has increased to 700 cells.
Calculators are not allowed on this exam. Express your solutions exactly
Ce mpoIC Jo i.e.
including logarithm expressions as necessary.
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—
(a) ‘Write the general differeiltial equation that describes time change in bacteria popu
lation over time.
(b) Write the function that describes the quantity of bacteria after t hours.
KP
Pe AT
P(
pt
7o6.-/Ooe
K
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(c) Find the quantity of bacteria after 2 hours. Your solution may contain logarithm
expressions but should not contain any variables.
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e
2Jfl (
(d) Given the initially population size of 100 cells how long will it take for the population
to reach 80,000? Your solution may contain logarithm expressions but should not
contain any variables.
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[15 points]
Exam
01, Page 8 of 11
25 September 2015
6. Work Needed to Stretch a Spring. A force of 20 N is required to hold a spring that
has been stretched from its natural length of 0.1 m to a length of 0. 15m.
(a) How
much
work is done stretching the spring from 0. lm to 0.2in? Set up tue
The integral is your solution
appropriate integral but do not integrate.
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to t&-L’oo k <- 0.i m —s’
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kx
L) ‘1
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k(,o)
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(b) How much work is done stretching the spring from 0.2m to 0.4m? Set up the
appropriate integral but do not integrate. The integral is your solution.
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ii 0I
Exam 01, Page 9 of 11
Mathi 320.001
[10 points]
25 September 2015
7. Direction Fields. Sketch the solution to the initial value problem on the appropriate
direction field
f.
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[15 points]
Exam 01, Page 10 of 11
25 September 2015
8. Volume of Rotation. Find the volume generated by rotating the region bounded by
the curves
= x
2 and x = y
2 about the line y = —2. You may use either the method
of disks/washers or the method of cylindrical shells. A graph of the curves has been
provided. The curves intersect at the points (0, 0) and (4, 2).
(4
1
prt?bQLW
(a) Begin by labeling the curves with the corresponding function.
(b) Next label the graph with the coordinates of the intersection points.
(c) Sketch the solid that results from revolving the enclosed region about the line y
—2 on the provided graph. Clearly label the line y = —2.
=
(d) Set up the integral for calculating the volume of the solid. Do not integrate. The
integral is your solution.
2
-
x
WS-Qr y.th.-Od
rz )(L +z ( ] Sx
0
J
xa+
l\iatlil32O.001
[5 (bonus)]
Exam 01, Page 11 of 11
25 Septeniber 2015
9. Find the volume of the solid described in Problem 8 using whichever method you did
not use in problem 8. Set up the integral for calculating the volume but do not integrate.
The integral is your solution.
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