Math 28
1.
Express in simplest factored form:
a)
2.
Review for Appendix A, Chapters 1, 2, and Appendix D
x 2 ( 1 )( x 2)3 (4) + ( x 2) 2 (6 x)
2
( x + 5)2
For the function f ( x) =
1
x 2 ( 1 ) ( x 2) 3 (4) + ( x 2) 2 (6 x)
2
( x + 5) 2
value(s) of x such
Math 23
REVIEW
Part I: Problems
1.
A firms fixed cost is $260,000; it costs the firm $77 to make each unit of its product; and it sells each unit
for $90.
a) Find its cost, revenue, and profit functions.
b) How much does each unit made and sold contribute
Math 28 2-3a Polynomial and Rational Functions Supplement
Spring 2009
1. For the following rational functions determine the x and y intercepts, the domain,
all asymptotes (vertical or horizontal), then sketch a graph.
a.
f ( x) =
x 5
x+5
b.
f ( x) =
4x
x6
Mathematics of Finance
Formulas
Simple Interest: i = prt
Amount with compound interest:
A = P(1 + i ) n
Amount with continuous compound interest:
or
A = Pert
FV = PV (1 + i ) n
or
FV = PV e rt
Annuity account into which a person makes equal periodic payme
3 MATHEMATICS OF FINANCE
EXERCI SE 3 e 1
Things t o remember :
1. SIMPLE INTEREST
I=Prt
where 1'2 interest
P= principal
r: annual simple interest rate expressed as a decimal
t = time in years
2. AMOUNT#SIMPLE INTEREST
A:P+Prt=P(1+rt)
2 amount or f
Mathematics for Business and Social Science (Math 28) Fall 2013
MTWTh 12:45-1:50,Room: TBA ( LS 203 or MC 71) (Sec. 2684)
Prerequisite: Completion of College Algebra (Math 26), or equivalent, with a grade of C or better
Instructor: Dr. McGraw
Office: Math
Supplement to Section 6.4 and 6.5
In this section starting on page 390 the book introduces the notion of left sum and right sum.
The left sum of n rectangles is denoted by Ln . The right sum of n rectangles is denoted by Rn .
It is left to the student to
Solutions for Supplement to Section 5.4
1)
B# B#
B#
B#B"
B#
Domain: a _ !b a! _b. No C -intercept. The B-intercepts are # ! and " !
Vertical Asymptote at B !
0 B
Horizontal Asymptote:
"
" B B#
"
B_
lim 0 B lim
B_
" HA at C "
Crosses horizontal asymptot
Math 28 Chap. 3.2 Inequalities Supplement
Spring 2009
1. Solve the following:
a.
x 7 < 25 x 5
b.
x2 6x
0
5 x + 15
c.
2x + 5 x +1
<
x +1 x 1
2. Find the domains for the following:
a.
f ( x) =
x4
x+6
b.
f ( x) =
x2 + 5x + 6
x 2 36
c.
f ( x) = x 2 25
Answers
Properties of Sequences
1.
n
c = cn
k =1
2.
n
ca
n
k
k =1
3.
n
(a
k =1
5.
n =1
n =1
- bk ) = ak - bk
a = a
k
k =1
n
+ bk ) = ak + bk
j
n
k =1
n
k
n
k =1
n
(a
k =1
n
k
k =1
4.
= c ak
k
k =1
+
n
a , where 1<j<n
k
k = j +1
Sum Formulas
6.
n
k = 1 + 2 +
Math 28
Review for Chapter 3
Find the following limits, if it exists.
x2 4 x + 1
x5
x3 + 8
x 2 x + 2
lim
5.
2 x 6,if x 4
lim f ( x) if f ( x) =
x 4
x 2, if x > 4
8.
x 3
a) lim
x 3
9.
3. lim
x 5 + x
If lim f ( x) = 5 and lim g ( x) = 9, determine the fo
Math 28
Supplement to Section 5.4
Below is a list of information considered pertinent to graphing functions. Depending on the type
of function (polynomial, radical, or rational), provide the following information.
Domain
Intercepts (x-intercepts only if
Math 28
1.
Review for Chapter 5
Given that h( x) = x 3 3 x 2 24 x + 34.
a) Find the intervals where h is increasing and the intervals where it is decreasing.
b) Find the intervals where h is concave upward and the intervals where it is concave downward.
c
Math 28
Review for Chapter 4
For problems #1 16, find
2x 1
e2 x
dy
in simplest factored form:
dx
1.
y=
5.
13x
f ( x) = 2
+ 25
x + 100
8.
y=
12.
y = xe x
2.
6.
2x +1
x2 1
2
x3
y = x 2 ln( x 2 1)
9. y =
13. y = ( x 2 + 3 x)
d2y
find
dx 2
3.
y = 2x
3
ln(
Elasticity of Demand
Any increase in price will cause a decrease in demand, the elasticity will tell us
approximately how much demand will decrease and what will happen to the revenue.
1. If E(p) = 1 then the elasticity is called unit elastic.
a. An incre
Math 28
Review for Chapters 6 & 7.1-7.4
1.
Find the total cost of the first 200 units of a product with a fixed cost of $500 if its marginal cost function is given
by G w B #& !%B.
2.
Evaluate:
#
$
&
( B B ( .B
3.
Evaluate:
B"
.B
(#
B #B &
4.
Find the fun