NorthWest Arkansas Community College
Division of Science and Mathematics
Syllabus
Course:
Math 2043, Survey Calculus
Credit Hours: 3 credit hours for transfer
Prerequisite: College Algebra with a grade of C or better or appropriate placement score.
Instru
Section 5.6, Integration by Substitution
Spring 2001, TV
Differentials
For a differentiable function f(x), the differential df is df = f ' ( x)dx
Examples:
U-SubstitutionAllows us to integrate a wide range of functions by basically reversing the Chain Rul
Survey Calculus, Section 5.5
Two Applications to Economics: Consumers Surplus and Income Distribution
TV s01
Suppose you could purchase a product for less than you were willing to pay. The savings between what you actually had
to pay and what you were wil
Section 5.4, Survey Calculus
Further Applications of Definite Integrals: Average Value and Area Between Curves
TV spring 2001
Average Value of a Function:
1
(Average Value of f on [a, b])=
ba
b
f ( x)dx
a
Average value = Definite integral divided by the
Survey Calculus, 5.1, Antiderivatives and Indefinite Integrals
Indefinite Integral
f (x)dx = g (x) + C if and only if
g ' ( x) = f ( x)
Rules of Integration
*
kdx = kx + C
*
x dx = n + 1 x
*
[ f ( x) g ( x)]dx = f ( x)dx g ( x)dx
*
kf ( x)dx = k f (
Survey Calculus, 4.4, Two Applications to Economics
Relative Rate of Change of f (t ) =
s01, TV
f ' (t )
d
ln f (t ) =
dt
f (t )
If application, if f (t ) is the price of an item at time t, then the rate of change is f ' (t ) , and the relative rate of ch
Survey Calculus
4.3 Differentiation of Exponential and Logarithmic Functions
Derivatives of lnx-
d
1
d
1
ln x = . More generally,
ln f ( x) =
f ' ( x)
dx
x
dx
f ( x)
In other words, the derivative of the natural log of something is 1 over that something t
Survey Calculus, 4.2 Logarithmic Functions
Definition
log a x = y is equivalent to a y = x (a>0)
Logarithms and exponentials are inverses of each other.
When evaluating logarithms ask yourself, to what power must I raise the base to get the argument. The
Survey Calculus, 3.4Further Applications of Optimization
2nd Derivative Test
Sometimes a quick way to test whether a particular critical value is a max or min.
To use the 2nd Derivative Test you, find the critical values, and plug them into the second de
Optimizing Functions of Several Variables
The point (a,b) is a critical point of f ( x, y ) if f x (a, b ) = 0 and f y (a, b ) = 0
To find the maxima, minima, and saddle points of a function f ( x, y ) we first find the critical points as follows:
1) Set
Lagrange Multipliers
Sometimes we need to optimize functions subject to some constraint. To solve such constrained optimization problems we use the
method of Lagrange Multipliers
To optimize f ( x, y ) subject to g ( x, y ) = 0 :
1) Write the new function
Survey Calculus, Exam #1
Chapter 2 and Sections 3.1 and 3.2
September 2 6, 2000
Name_
To receive full credit you must show all work.
1. Evaluate the following limits without the use of a table.
x 2 3x + 2
a. lim
x2
x2
1
b. lim s s
s 16 2
2. Use the defin
Survey of CalculusDepartmental Review Sheet
Fall 2005
(Brief Applied Calculus, 3rd Edition. Berresford, Rockett. Houghton Mifflin, 2004.)
All work should be shown and all answers should be exact unless stated otherwise. It is fine to leave
radicals in the
Survey of Calculus Final Exam Review Key
Fall 2005
1.
a. 6
b. 9
c. 1/4
2.
a. 3
d. 1,2
g. 1, 0, 2
b. 3
e. 1, 0, 2
c. 3
f. none
3.
a. 4x-3
b. 1/x2
4.
6. ii. a.
b.
c.
d.
e.
y = -6x+2
(0,0), (4, 256)
Inc: (0,4) Dec: (-,0), (4,)
Rel Max: (4, 256) Rel Min: (0,0
NorthWest Arkansas Community College
Division of Science and Mathematics
Fall 2005
Course Outline
Course:
Math 2043, Survey of Calculus
Catalog Description:
A survey and applications course in calculus designed for students in business, life sciences and
Survey of Calculus
2.1
Fall 2002
Smith
1
Limits and Continuity
Limits
There are basically three ways to evaluate limits:
(1) _
(2) _
(3) _
I. Evaluating limits graphically.
A. The limit of f(x) as x approaches a certain number, c, is the _ that the functi
Survey of Calculus, Exam #3
Sections 5.2 5.6 and 7.1,2,3,5
December 7, 2000
Name_
Please show all work ON THE EXAM PAPER to receive full credit. Each problem is worth a total of 9 points. I will count
the best 11 of 12 to calculate your exam score.
1. Int
Survey Calculus, Exam #2
Section 3.3 5.2 (primarily)
February 14, 2001
Name_
Please show all work to receive full credit.
dy
1. Find
for each of the following: (7 each)
dx
a. y = 3 x 4
3
2 x 2 + 5x + 1
(
b. y = x 3e 3 x + ln x 2 2 x
)
c. 2 xy 2 + 3x 4 y =
3.3Optimization
TV spring 2001
The absolute maximum of a function is the largest y-value that the function ever attains. The absolute minimum of a function
is the smallest y-value that the function ever reaches. An absolute extreme value is either an abso
3.1Graphing Using the First Derivative
TV, Spring 2001
A function f ( x) has a relative maximum value at c if f (c) f ( x) for all values of x near c. In other words the point
(c, f (c) is a peak of the graph.
A function f ( x) has a relative minimum valu
Survey of Calculus Exam #3
Fall 2004
Name _
You must show all your work on this paper. Solutions without correct supporting work will not be accepted.
Please circle your answers. You may omit one problem by clearly writing OMIT by the problem. If you do
n
Survey of Calculus Exam #2
Thursday, October 21, 2004
Name _
You must show all your work on this paper. Solutions without correct supporting work will not be accepted.
You must omit one problem by clearly writing OMIT by the problem number. If you do not
Survey of Calculus Exam #1
Thursday, September 16, 2004
Name _
You must show all your work on this paper. Solutions without correct supporting work will not be accepted.
1. Use the graph given to evaluate the limits: (3 points each)
a. xlim+ f ( x ) = _
2
Survey of Calculus Section 5.3
You know how to find the area of some regions such as rectangles, circles, triangles, etc. In this section we will learn how
to find the area of irregular shaped regions. We will do this by approximating the area with rectan
Survey of Calculus Section 4.1 Exponential Functions
You did much more with exponential functions in algebra than we will do here. Of course, you already know
what an exponential function is and how to graph it. We are primarily interested in how to apply
Survey of Calculus Section 3.6 Implicit Differentiation and Related Rates
Until now all the functions you have seen in this class have been written explicitly. That just means that y has
been isolated. Now we will learn how to find the derivative when a f
Survey of Calculus Section 3.2 Graphing using the 1st and 2nd Derivatives
Recall: Use the 1st derivative to determine:
1) where a function is increasing/decreasing.
2) the critical points.
3) the relative extrema using the 1st derivative test.
Now we will