IViath 1320.001 Exam 01
Fall 2015
Name
O
Student ID Number:
Thm A
Class Number:___________
Instructions:
• Please remove headphones and hats during the exam
• 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 iii sin plified form 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!
-
1\’Iathl32O.0O1
Exam 01, Page 2 of 11
For Grader Use Only
Q iiestion
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
25 September 2015
Exam 01, Page 3 of 11
Matlil32O.O01
WRITE YOUR ANSWERS IN THE PROVIDED BOXES
SHOW YOUR WORK
[11 points]
1. Arc Length.Fiiid the exact length of the curve defiiied by:
L.
=
2
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+0
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for 0 <y < 3.
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iViath 1320.001
[15
points]
Exam 01, Page 5 of 11
{
25 September 2015
3. Separable Equations. Solve the following initial value problem:
dy
6x(y
—
—
1)2
LoAr o44I1,
1
y(0)-
—
The solution should be expressed as an explicit
_—d
2
(j—i)
function of
y. (i.e. in the form y(x)
=).
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Mathl32O.001
[12 points)
Exam 01, Page 6 of 11
25 September 2015
4. Area Between Curves. Find the area enclosed between the parabola y
2
line y = 2x. A graph of these curves has been provided.
=
8 and the
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(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.]
)
L2.)(
)(2
4x2.?x
(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.
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-=
iccs j-)ch
Mathl32O.001
[12 points]
S
1’0
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 500 cells.
Calculators are not allowed on this exam. Express your solutions exactly
i.e. including logarithm expressions as necessary.
.
..
.
.
—
.
(a) Write the general diflerential equation that describes the change m bacteria popu
lation over time.
(b) Write the function that describes the quantity of bacteria after t hours.
e 5ooIooeI<’ kJ()
0
P(#P
P(
(c) Find the quantity of bacteria after 3 hours. Your solution may contain logarithm
expressions but should not contain any variables.
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SJh()
(d) Given the initial population size of 100 cells how long will it take for the population
to reach 10,000? Your solution may contain logarithm expressions but should not
contain any variables.
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iOOOO
Jn(it)
ioôe
—,
,ooe
lVIathl32O.001
[15 points]
Exam 01, Page 8 of 11
25 September 2015
6. Work Needed to Stretch a Spring. A force of 25 N is required to hold a spring that
has been stretched from its natural length of 0.1 in to a length of 0.l5in.
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bxtbool(
(a) How much work is done stretching the spring from 0.lrn to O.2m? Set up the
appropriate integral but do riot integrate. The integral is your solution
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coo
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f
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0
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1
5OOX°
(b) How much work is done stretching the spring from 0.2in to 0.3in? Set up the
appropriate integral but do miot integrate. The integral is your solution.
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Matlil 320.001
Exam 01, Page 10 of 11
25 September 2015
[15 pointsj
Cb,Y1 0
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 x = —2. You may use either the method
of disks/washers or the method of cylindrical shells. A graph of the curves has been
C
provided. The curves intersect at the points (0,0) and (4,2).
ptob4Ln
(0?;, *
2x
xT
(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 x
—2 on the provided graph. Clearly label the line x
—2.
=
(d) Set up the integral for calculating the volume of the solid. Do not integrate. The
integral is your solution.
—
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Matlil32O.O01
[5 (bonus)]
Exam 01 Page 11 of 11
25 September 2015
9. Find the volume of the solid described in Prohleiii 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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