Week 2 Knowledge Check Study Guide
Concepts
Risk
Mastery
Questions
100%
1
100%
2
100%
3
Fallacy
100%
4
Rhetorical Device
100%
5
Making the Choice
100%
7
Psychological Biases
100%
8
100%
9
Decision Making in
Groups
Potential Problems of
Using a Group
The F
MAT 210: 13.3-13.4
Riemann Sums: a method to estimate area under a curve using rectangles of equal widths.
For this course, typically left rectangles are used.
Example: estimate the area under
f (x )=3 ex on the interval [0,10] using 4 left rectangles. (n
MAT 210 Midterm Exam 2 Information: 12.1 12.6, 13.1-13.2. Other Classes will include 13.3 and
13.4
What should you be able to do for the test?
Derivative Applications:
Be able to solve implicit and logarithmic differentiation problems
find local and abs
Derivatives and other Mathematical Rules
ln( a b) ln a ln b
1
x 1
x
a
ln ln a ln b
b
e 2.71828 is a number
d n
x nx n1
dx
d u u ' v uv '
dx v
v2
e x or e g(x) is a variable
u f x,v g x
d
uv u ' v uv '
dx
ln a r r ln a
d n
u nu n1 u '
dx
d
a x a x
Name: _ Class: _ Date: _
MAT 210
ID: A
TEST 2 REVIEW (Ch 12 and 13)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. The population P is currently 10,000 and growing
at a rate of 7,000 per year. What is the
University of Phoenix Material
Final Grammar Test
Part I: True or False
.1 The following word group is a FRAGMENT: That movie,
one of my favorites.
_X_True
_False
.2 The following word group is a FRAGMENT: The local
baseball team, needing a good pitcher m
Week 1 Knowledge Check Study Guide
Concepts
Mastery
The four functions of
management
Questions
100%
1
2
3
100%
4
5
6
100%
7
8
9
100%
10
11
12
100%
13
14
15
The role of organizational
behavior
Score: 15 / 15
The nature of personality
and the Big Five
perso
Week 1 Knowledge Check Study Guide
Concepts
Mastery
Purposes of law
Questions
100%
1
2
3
100%
4
5
6
100%
7
8
9
The role and structure of
the American judiciary
Forms of alternative
dispute resolution
Score: 9 / 9
Concept: Purposes of law
Mastery
100%
Ques
MAT 210: 12.3 12.5
(12.3) Second Derivatives
A second derivative tells us how the derivative of a function changes. There are no new rules for
calculating 2nd derivatives, just take the derivative of a derivative function!
Interpreting the second derivati
12.1-12.2: Maxes, Mins and Optimization
Suppose that a business' cost to produce x computers is given by C x =14000100 x0.01 x 2 .
How many computers should they produce to minimize the average cost per computer?
Recall: average cost = C x =
C x
14000
100
FALL 2012
MAT 210
Instructor: Woonjung Choi
Office: ECA203
SLN: 72356 (9:00AM), 72358(12:00), 72359(1:30)
Tentative Office Hours: TTh 10:20-11:10 and T 2:50-3:15,
or by appt
Place: SS 229(9am), PSF101( 12:00, 1:30)
E-mail: woonjung.choi@asu.edu
Course des
Limits: Numerical and
Graphical Approach
Limits: Numerical and Graphical Approach
lim f ( x) = L
x a
x
2.9
2.99 2.999
f(x)
4.61
4.96 4.996
3
3.001 3.01
3.1
5.004 5.04 5.41
lim
x 3
f ( x) = 5
Limits: Numerical and Graphical Approach
lim f ( x) = L
x a
If f
Limits and Continuity
Limits and Continuity
Definition: Let f be a function. Then we say f is continuous
at x = a if and only if
i) f (a ) exists
(This means a is in the domain of f.)
lim f ( x) exists (This means there exists a finite limit at x = a. )
(
Limits and Continuity:
Algebraic Approach
Limits and Continuity: Algebraic Approach
Goal: This section will focus on algebraic techniques to evaluate a limit.
Question: When evaluating a limit, why do we need algebraic
techniques?
Answer:
There are times
The Derivative:
Algebraic Viewpoint
The Derivative: Algebraic Viewpoint
Goal: Find the exact value of the derivative.
The definition of the derivative at x = a is
f '( a ) = lim
h0
The definition of the derivative for the function f is
f ( a + h) f ( a )
Derivatives of Powers, Sums
and Constant Multiples
Other Notations
For y = f ( x ) ,
f '( x ) = y! =
d!
#
dx "
D#
$
dy df
d
=
=
f ( x ) = Df ( x ) = Dx f ( x )
dx dx dx
:differentiation operators
process of calculating a derivative
dy
f !(a ) =
dx
dy !
=#
1/31 Week in Review: 10.5-10.6
Average Rate of Change: slope between 2 points
Instantaneous Rate of Change: slope of a tangent line (this is a derivative value)
Example: let f x =3 x 22 x 1 .
a) Find the average rate of change of f(x) on the interval [0,2
10.1 10.2: Limits & Continuity
Definitions:
lim f x
f a is an expression for the value of the output value of
is an expression that gives the trend or tendency of the output values of
f x as x approaches a.
x a
f x at
x=a
The two expressions above may or
MAT 210 Review 2/7: 11.1-11.2
d n
x =n x n1 . This works for ALL numerical exponents n. If you can re-write
dx
an expression as a power of x (with a coefficient is fine as well), then you can take its derivative using
power rule!
Recall power rule:
Examp
10.3 10.4: More Limits and Average Rate of Change
Another limit with piecewise-defined functions
Remember that a limit value and a function value are the same if and only if the function is continuous
at the x value in question.
cfw_
f x = 47 x if x3
5x 2
11.3-11.4: Product, Quotient & Chain Rules
Product Rule:
Quotient Rule:
Chain Rule:
d
f xg x = f ' x g x g ' x f x
dx
f ' x g x g ' x f x
d f x
=
2
dx g x
g x
d
f g x = f ' g x g ' x
dx
d
du
f u = f ' u
dx
dx
also written: for u, a function of
11.5-11.6: Exponential, Logarithmic & Implicit Derivatives + test info
Basic Rules
d
1
logb x = x ln b
dx
d
1
log bx= x ln b .
dx
It doesn't matter if there are are abs value signs or not the derivative is
the same. Only the domain of the function chang