Document 12044511

advertisement
2 December, 2013
Chapters 12—13 Review
Math 1100
Name:
The cluestiolls below are intended as a partial review. You should also refer to
your written homework and quizzes (and, to a lesser extent. your \VebAssign
work) as you study for the exam.
1.
(a) What is an indefinite integral?
ri-
ae4_e
-I
F(x)
o
Sv&1
b—er
,
,‘
,
(b) What is a definite integral?
T1- 21-e
01 P)
tnta
ctii
t€j.t
x
9v
o
kb
i—i-i
x)
X—ctx,’.s
L
Ac
C’
(c) How are definite integrals and indefinite integrals related?
J@
F(x)
;
{‘—-
,-kf,iI-
w1i—eyAI
) -F()
o1
h—e
J
f
cb
çcN
cI
II
0
‘4
x
k
9-
•1<
><
CD
C”
I•l
r
—
H
>(I
“
+
3<
>c
1
C
C))
0
CD
CD
E
CD
CD
C))
crq
CD
CD
CD
Cl)
LDI
+I
CD
0
0
—
1
)Cr3
CD
-t
P
CD
CD
CD
C.—,
—
)c•
0—
.:z
c____,
‘I
-
‘<I
D
‘—
Izi
I—’
3
I’
“4
1
N
-
cr1
a-.
+
Hi
0
LJ
-
‘I
r
r.j_
0
>
>
(3
L
_JI
-
0
8
3. Find each area shown or described below.
(a) The area enclosed by the curve y
a; =
=
2 + 1. the i-axis, and the lines x
x
and
=
z.
((z)-7
(;( ,)3
)
rzJ
(b) The area enclosed by y
number.)
2
I
=
—4x and the i-axis. (Your answer should be a positive
3
4x
I’o
I
X
Q
3
x d
10’)
[((b)7
e
—t
t
(o)
x2iT’
-z
2
XLZZ
=
2
—a;
—
2x + 2. (Not pictured)
(x-x
-
z)
r)
X’4—Zic
2
1
.L
x —2
QY
0
r9
04-I 4-I -O
(c) The area enclosed between y
X’—Z
(i-
fo -(-I)J(()J
a
Li 4-cchans;
() ((-I)z()’)J
t.c ‘(
L-??1i
-t
-A
3
K4-1xJ
-l
(t)
c-’
•1
(
—
t
>(
—
r-)
1
+
-t—
r%)
-
N
1-
r
-I
1
ra
N
7
-r
—En
C
CD
C
CD
CD
CD
CD
+
H
II
CD
C
C
CD
CD
C
C
CD
CD
0
CD
0
CD
C
CD
CD
CD
CD
CD
5. Suppose the marginal revenue for a product is MR = 900 and the marginal cost is
MC = 3O/x + 4 with a fixed cost of $1000 (that is, it costs $1000 to produce 0 units).
(a) How many units should be produced to maximize profit?
d
c
q)o—3OJi
oo_!crq
oo
4-
rej,
-
(ñ
(ft):
9t2Ox- C
ZO
R()
O
(
4
ff)Q.Q
O
oc
4
rq (
(b) What is the profit or loss from producing 5 units?
5i
,t
IOC’
it
1000
/Z
3
()
Zo
/z
3
)
1
(
ioD 1OfrC—
L1C) (
a
OK— ZO(xi) ui
P(?cY (9
-‘-
iO
-
qsO
3)2O.
,
Download