Math 1160 Elementary Applied Calculus, Fall 2016
Prefinal Exam
Name:_
KSU #:_
Questions from 1 to 5 are similar to those in unit tests 1 to 5
Given demand function D( x) x2 12 x 36 and supply function S ( x) x 2 12 . Solve
questions in #6, 7 and 8
6. Fin
Math 1160 Elementary Applied Calculus, Fall 2016
Pretest 5
Name:_
KSU #:_
1.
10e
a)
0.5 x
dx =
0.5e0.5 x c
Correct answer: c)
b) 10e0.5 x c
10e
0.5 x
c) 20e0.5 x c
e0.5 x
dx 10(
) c 20e 0.5x c
0.5
2. Find a function f ( x) such that f '( x) 3x 5 and f
Unit 3 Discussion
Ashley Stephens
Henry County
Est. Population: 203,922
Annual Percent Change: 5.4 or dt/dp 0.054P
1. P(t) = 203922e^0.054(t)
2. P(t) = 203922e^0.054(6) = 281,952.20. This means that sixe years after
2010(2016) there will be a population o
Ashley Stephens
Unit One Discussion
Problem # 6
Numerically
x
F(x)= (2x^2x21)/(x^2x12)
2.96
1.8563
2.99
1.8569
2.999
1.85699
Graphically
Algebraically
To solve my problem algebraically, I had to start by factoring. I factored the
numerator by group
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
Fall 2016
1
5.2 Exponential Functions and Graphs:
Exponential Function:
The function () = , where is a real number,
> , is called the exponential function,
base a.
The following ar
5.1 Inverse Functions
Fall 2016
1
5.1 Inverse Functions
Inverses:
When we go from an output of a relation back to its
input or inputs, we get an inverse relation.
When that relation is a function, we have an inverse
function.
Interchanging the first and s
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
Fall 2016
Logarithms:
loga 1 = 0 and log, a = 1, for any logarithmic base a.
log,x = y <> x = a"'
A logarithm is an exponent!
Example 8:
Convert each of the following to a logarith
5.1 Inverse Functions
Fall 2016
Example 4:
Show that f(x) = 2x 3, is onetoone, and if it
is, find a formula for f (x).

0
/
Ak )
t
4 C( _b
3
14
Z
r1
(ac)
?
b
3
_x

5.1 Inverse Functions
Fall 2016
1)
)C
Ij
7c
3) 5,0
/
(3 .
77
L9Sf
ttj
fc
5.1 Inverse
5.1 Inverse Functions
Fall 2016
1
HorizontalLine Test:
If it is possible for a horizontal line to intersect the graph of
a function more than once, then the function is not onetoone and its inverse is not a function.
not a onetoone function
inverse is
5.5 Solving Exponential and Logarithmic Equation
Fall 2016
5.5 Solving Exponential and Logarithmic
Equation:
Solving Exponential Equations:
Equations with variables in the exponents, such as
3x20 and 25x=64,
are called exponential equations.
Use the follo
3.3 Analyzing Graphs of Quadratic Functions
Fall 2016
Example 6:
A stonemason has enough stones to enclose a
rectangular patio with 60 f t of stone wall. If the
house forms one side of the rectangle, what is the
maximum area that the mason can enclose? Wh
5.4 Properties of Logarithmic Functions
Fall 2016
5.4 Properties of Logarithmic Functions:
The Product Rule:
For any positive numbers M and N and any
logarithmic base a,
loga MN = loga M + loga N.
(The logarithm of a product is the sum of the
logarithms o
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
Fall 2016
Example 12:
Describe how the graph of
f(x) = 3 Inx
1
2
can be obtained from the graph of y= in x
Give the domain and the vertical asymptote of
each function.
"
\J ,
COLJ1
5.5 Solving Exponential and Logarithmic Equation
Fall 2016
1
5.5 Solving Exponential and Logarithmic
Equation:
Solving Exponential Equations:
Equations with variables in the exponents, such as
3x = 20
and
25x = 64,
are called exponential equations.
Use th
Section 5.5 Right Triangle Trigonometry
In section 5.3 we were introduced to the sine and cosine function as ratios of the sides of a
triangle drawn inside a circle, and spent the rest of that section discussing the role of those
functions in finding poin
Section 1.3 Rates of Change and Behavior of Graphs
Since functions represent how an output quantity varies with an input quantity, it is natural to ask
about the rate at which the values of the function are changing.
For example, the function C(t) below g
Test1StudyGuide
Math 1113
Precalculus
Kennesaw State University
Instructor: Steven Riley
Name_
README!
Alrightguys&gals!HereisyourStudyGuide.Iwouldsuggestworkingeachproblembyhandonaseparatesheetof
paperBEFOREreviewingyouranswers.Thisstrategyhasproventobet
Practice Final Exam
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the limit exists. If it exists, find its value.
1) lim f(x)
x 0
A) 2
1)
B) Does not exist
C) 2
D) 0
2) lim f(x)
x 1
0.1
Practice Final Exam Solutions
1. b; limx!0 f (x) does not exist because limx!0 f (x) =
1
1 and limx!0+ f (x) =
2. d; we can see from the graph that limx!1 f (x) = 1
3. b; True; limx!4 f (x) =
1 and limx!4+ f (x) =
1:
4. a; True; the graph shows that l
Kelsey Lot
Group Discussion: Question #4:
The work should include a graph, an inputoutput table, and algebraic solution.
Limit: x 2 . x^38/x2
Limit Numerically.
I.
x 2 (x^38/x2)
F(2)=
1.
2.
3.
4.
5.
(2)^38/(22)
88/22
0/0
Limit does not exist. Now
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