Math 1220-002
Midterm #1
Spring 2012
September 24, 2012
Midterm #1: DEQ’s, Advanced Differentiation
& Integration Techniques
Instructions: You may use a calculator to assist you with any arithmetic, a writing
utensil, and your 3x5 reference card that you have prepared. No other materials
are permitted. Please show all of your work to the level of detail that is specified
in the instructions for that particular problem. You MUST write your final answer
in the space provided to receive full credit. The point value of each problem is
specified in the problem statement. Most of the credit will be awarded for doing
the calculus correctly and showing the appropriate steps. A correct final answer
with no work supporting it will receive very few points!! You may turn in your
exam and leave when you have finished.
Recommendation: You do not need to work on these problems in order. I would
suggest first answering the ones you find the easiest. Then go back and work on
the harder ones at the end. Also, if you finish early I would suggest double
checking all of your work, just in case you made any very simple mistakes.
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Math 1220-002
Midterm #1
2.
Spring 2012
September 24, 2012
In the year 2000, the population of South Park, CO was 500. If the population of South
Park doubles every 12 years, how long will it take for the population to triple? Assume
that the population of South Park grows exponentially. Show all of your work and write
your answer in the box below. (10 points)
Tripling Time
years
=
5dO
p(
/S-w
3
3P
s
)
\AJ
P(123 OOO
5d0g
)2
0.037761;
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Spring 2012
September 24, 2012
Math 1220-002
Midterm #1
Solve the following differential equations using the integrating factor technique or
3.
separation of variables. Use the given initial condition to solve for C. Write your final answers
in the boxes but show all of your work in the space below. It is NOT necessary to simplify your
answers algebraically. (20 points)
x
P1x*
(a)
+-y=x
1
y
2
=
y(x)
10
=
()
.3
(7
3
I
y)2
y
o (‘)
3
x
y’
=
y(O)
x
2
5y
.._i__j
_4
LI
(b)
£4
=
10
y(x)
=
/
y(x)
Cs
2
LL
2-
Math 1220-002
Midterm #1
Spring 2012
September 24, 2012
4.
Use familiarity, algebraic simplificaç, or u-substitution to solve the following integrals.
Write your final answer for each problem in the boxes but show all of your work in the
space below. (20 points)
(a)
f
cosh(/)d
Li
dv
c
ck (u)
tv
1EZEc
(b)
c
j
1
+6x+1O
2
x
dx=
[HINT: Complete the square]
q(
S
—
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Spring 2012
September 24, 2012
Math 1220-002
Midterm #1
I:
Use integration by parts or tabular integration to solve each of the integrals below.
5.
Write your final answer for each problem in the boxes but show all of your work in the space
below. (20 points)
os (2x)dx
fx
c
3
(a)
=
Lv
x
L S (2 .‘)
-
v(2)
S
9
,
o t_
f
(b)
sin (3x)dx
e
”
2
2x
U
SN
3)\
3coSLx)
-.
e
=
su
-
;v)(31)
I22x
()—
c()
-
f
+C
i2Ic (o;(3)
3fZ
;1)- Qcca()
4
Math 1220-002
Midterm #1
Spring 2012
September 24, 2012
Use trigonometric substitution, u-substitution, or trigonometric identities to simplify
6.
and solve the integrals below. Write your final answer for each problem in the boxes but show
all of your work in the space below. (30 points)
(a)
(3x)dx
3
fsin
1
=
-
u 3x
dx
u)
2
i Vcs(u)
c’! _((jj4)
)
(J3?c
1\L+
cs1v)
(v)
( d)
(osu))
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—
c
çtviç
vi1)dj
Lv
2
y
CO(u)
c(jLv
+
(b)
f_c1x=
dx
e
2;
.
X
3&o
C
C dx
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