Class ID:
Name:
o\S
MATH 1210-008
Midterm 2
U
FaIl 2012
November 8, 2012
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SHOW ALL. WORK. As partial credit will be given where appropriate, and there
may be NO credit given for answers without supporting work.
Scratch paper will be provided by the instructor. Scratch work will not be
graded, record all work that is part of your solution on this exam.
Make sure your work is organized and legible.
Answers should be simplified, unless otherwise indicated.
Box or Circle your final answers.
NO CALCULATORS, NOTES, PHONES, ETC.
You may use a 4x6 index card for reference.
bo NOT write in the table.
Prob. Score
1
/10
2
/30
3
/10
4
/15
5
/15
/10
6
7
/10
8
/30
Total
/130
1. Find
given 2xy
3
(Solve for
r
dx
—cos(xy)
=
5x —2.
but don’t bother simplifying any further.)
-‘
(
-
+
2(’)
2#
‘)
+
+
=
-
,
—
S dx
2. Evaluate each indefinite integral.
a) f(4&_—-÷cosx_12)dx
S
—‘
-
-\2’
-
‘
Answer 2o:
L
r
42_
\2-c s-C.
b) fx6./2x7_1odx
V’’3)
-
1
v2.c-)
‘
,•
Answer 2b:
c)f
d
3
v
-
I_
7)
2\ 2’,
—
—7
._f,_
4-ic,)
j
..2
2-2 I
2
Answer2c:
—
3
-
:
0
D
>
w
cy
(1
p
‘
‘I
‘5’
p
C—’
cflI
hi
hi
I.
II
4. Sand is pouring from a pipe at a rate of 8 cubic feet per second. If
the falling sand forms a conical pile on the ground whose height is
always I of the diameter of the base, then how fast is the height
increasing when the pile base has a radius of 4 feet?
2r
at
(-‘)
N
S
ak
N
dli
dt
-
2
5. Jon would like to make three identical enclosures adjacent to his
garage each with 9 square meters of area. The fencing for the outer
sides of the enclosures is stronger and costs $4 per meter, but he will
use fencing that costs only $2 per meter to divide the three
enclosures (refer to the figure below). What is the total cost of the
fencing for the least expensive enclosures?
(-)(i.)
N
c4-
4
4
r
‘ç
Vl
‘N
4
N
N
.4..
I
+
—
2
( -)
-
—
*rn i r
6
Q: 12(3)4 \2(’3)
YI
•%2’
:)
Cost
4
\os ,c’
_
6. Solve the following differential equation.
6
y
given
y
=1
when t = 2
-
-S rC
3
_-
-s\\
-
L1-
-s-c
5
C
I
7. Find the linear approximation for f(x)=-sEi at a 3.
z
I
(x#\)2
2
()
2-1
(s)
c()
..2
I
8. For f(x)
Given:
x
f(x)=
—.
x
answer the following questions.
and
2
(x)=
1
f
t
2x
+
3
4
x
a) brow the sign line for f(x)
—
I
‘I
b) Find all the local minimum and maximum points, if they exist, or state that
they DNE.
ç(’):
Local Max point(s):
Local Mm point(s):
c) brow the sign line f or f”(x)
+
3
d) Find all inflection points, if they exist, or state that they DNE.
I
-ii:
(o)
DNt
Inflection point(s):
(
2,
o
e) What is the domain of f(x). Write your answer in interval notation.
bomain:
(_o,
&) J
(,x)
f) Find the asymptotes, if they exist.
-
I
(%)
4
.x-o
‘)(
i-co
0
-1-I
-
Vertical asymptote(s):
Horizontal asymptote:
2
2
7(Extra Credit) Oblique asymptote:
g) Sketch the graph of f(x)
=.S,(
3