PRACTICE MIDTERM 1
Math 1220 sec 006
XXX
1i
I~—
Name:
—~
by writing my name
swear by the honor code
Read all of the following information before starting the exam:
• Show all work, clearly and in order, if you want to get full credit. I reserve the right to
take off points if I cannot see how you arrived at your answer (even if your final answer is
correct).
• No calculators, notes or books are allowed for this test.
• Please keep your written answers brief; be clear and to the point. I will take points off for
rambling and for incorrect or irrelevant statements.
• You have 100 minutes to work on the exam.
• The practice exam has 5 problems and the actual exam has 6 problems. Prepare accord
ingly.
• Remember to bring/show your ID during the actual exam.
• Good luck!
Problem (value)
1_(20_points)
2_(10_points)
3 (10_points)
4_(10_points)
5_(10_points)
Total (60 points)
Score
1. (20 points)
PRACTICE EXAM 1 Short Answer. For True/False questions you must write
‘True’ or ‘False’ and justify your answer.
a.
(4 pts)
b. (4pts)
True or False. sinhx
Evaluate
f
~4t
IL+
=
o~k~
+a~i
c. (4 pts)
Calculate ~ if f(z)
=
~
C
~cos(5X)
c~j~x) ~
d. (4 pts)
What is
S
e. (4 pü)
J’ ~du?
~c1vt
Prove a~’aY
=
fit
~
x4~c~
x ~
-
-e
2. (10 points) PRACTICE EXAM 2 At t = 0, a tank contains 100 gallons of saltwater,
holding 50 pounds of dissolved salt. Saltwater containing 3 pounds of salt per gallon is pumped
into the tank at a rate of 5 gallons per minute. Saltwater flows out of the tank at the same rate.
Assuming perfect mixing, find a function that expresses the amount of sait in the tank for t> 0.
)( (1);
~st3
I
~fl
an~i.~
~c
p
f4~
k&~ ~≤O
n~(\
X
—
H
+
~n
~#0
€
Di
cn~’c.
0 7)40’ ~/J—~
(eG1&~rt S
cit
e
3oc, ~
x:
300 ~
~;
I
3o~
2g~
3. (10 points) PRACTICE EXAM 3
a. (5 pts)
1
Evaluate f(t + 7)e2t+3dt.
2t ~ 3
dv
-
~
e
&tf) ~
2t#-3
b. (5pts) Evaluate fsec3xdz.
(hint: f sec(x)dx = in Isec(x) + tan(z)I)
uts~(x)
~7lj4t cec(~4-ctn(~)ckic
S~c&) 4-a~)
5
1~n~c)
(sQcôr~i ~ort&)) C%A
SCCk
k
5~
k
ç
2
Sec~
cec~cLic
~
6
v-~y
k
+
4.
(10 points) PRACTICE EXAM 4
a. (5 pt~s)
Evaluate ~‘16dx
f
A
+
+
~
See
~
~kct&4
1~r
Evaluate
44
A~
~1t~
(~
b. (5 pts)
~
-
~
-13
~
t~;7~ ~
~ i~i~-~I
f ~2~’;712dx
4
t
A(3et,)
-to
f5~xt3~
i~@)
=
A (o3
-~
)
—
~?~-y-ii
iot
7 )
~
7
—
~3J
I
)
~-‘~
~
+
~a
-~
5.
(10 points) PRACTICE EXAM 5
a. (5 pts)
Find f’Qr) if f(z) = tanh(x).
t4n
~
h1~)~;
X~
e Cv>.) e (
)~ ~ )~i (~f~c~
~
fl.): ~
-
jJrN
~
-I ~
b. (5 pts)
Derive a formula for the doubling time of a bacteria population governed by
the equation P(t) = P0e’t where /c > 0. (You must show all your steps to receive credit not
just write down a formula remembered from class.)
-
p~:Zp3 ~‘P0e
2e
c.~e’k ec,r
LI
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+
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a.
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c41(-’~ ~
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