Computer Science Rocks!
David Perez
11-Nov-12
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Fun with Excel!
This workbook contains 12 different sheets (not including this sheet) of some cool Excel features and functions.
Before you get started, be sure to add your name to the Excel properties as the author.
Be sure to work through all 12 sheets.
Fun with Excel!
This workbook contains 12 different sheets (not including this sheet) of some cool Excel features and functions.
Before you get started, be sure to add your name to the Excel properties as the author.
Be sure to work through all 12 sheets.
Excel Practice
This practice file will give you an idea of the layout and format of our Excel exam.
Tasks on this practice come from the online material and the book. Some are straight
forward, and some require you to use your problem solving skills to fi
9.1: Limits pg 1
9.1: Limits
The limit deals with what a function value,
, appears to approach as gets close to a
particular value.
What is f(x) as x 1 ?
7
6
5
4
3
2
1
-2
-1
1
As approaches 1 from either side,
2
3
4
x) approaches 3.
f ( x)
5
Notation: li
Section 9.2 Continuous Functions, Limits at Infinity
Intuition => a continuous function can be drawn without lifting the pencil.
A function f is said to be continuous at the point = if the following conditions
are satisfied:
(1) f (c) exists
(2) lim f ( x
Section 9.3 The Derivative: Rate of Change; Tangent to a Curve
Algebra Review: Finding Slope and Equations of Lines
Slope: Rate of Change Slope:
=
The slope of the line through two points
=
,
and
=
,
is given by:
Exam
Section 9.4 Derivative Formulas
Rules to Recall:
Negative Exponent Rule
Rational Exponent Rule
The Power of x Rule: If f ( x) x n , n , then f ( x) nx n1 .
o
o
()
()
()
o
The Constant Function Rule: If f ( x) c , then f ( x) 0 .
()
o ()
The Coefficient
Section 9.5 Product & Quotient Rules
Dx [u( x) v( x)] u ( x) v( x) , but Dx [u( x) v( x)] u ( x) v( x)
Consider u( x) v( x) x 3 , u v x 6 , Dx (u v) 6 x 5 , but u v 9 x 4 6 x 5
The Product Rule: If f ( x) u( x) v( x) , both differentiable, then
f ( x) u(
Section 9.6 The Chain Rule and Power Rule
Definition: The composite function, g of f, is the function ( g f )( x) g[ f ( x)]
The domain of g f is the subset of the domain of f for which g f is defined.
Ex. Let f ( x) 2 x 1 and g ( x) x 2
( g f )( x) g (2
Derivative Rules
The Power of
Rule: If f ( x) x n , n , then f ( x) nx n1 .
The Constant Function Rule: If f ( x) c , then f ( x) 0 .
The Coefficient Rule: If u is differentiable and
f ( x) c u( x), c , then f ( x) c u ( x) .
The Sum (Difference) Rule
Section 9.7 Using Derivative Formulas
Dont forget ALL of the derivative rules. In 9.7, all of the rules come together.
o Examples
1.
y
( x 2 3) 4
x
y
x(4)( x 2 3) 3 (2 x) ( x 2 3) 4 (1)
( x 2 3) 3 (7 x 2 3)
x2
x2
4
5
7
2. y 3x (2 x 1)
y 3x 4 7(2 x 5 1) 6
Section 9.9 Applications of Derivatives in Business and Economics
Notation:
MR instead of R( x) for Marginal Revenue
MC instead of C ( x) for Marginal Cost
MP instead of P( x) for Marginal Profit
()
()
Recall:
()
The marginal revenue is an estimation of t
Math 144 Exam 1 Outline
Exam 1 will cover chapter 9. This is not an exhaustive list. Your study tools should consist of: your notes,
blackboard, the textbook, the homework, SI, study groups and office hours. Make sure that you work
through all of the home
Practice Exam KEY
Do not limit yourself to only this practice.
1. Find the limits if they exist. If the limit does not exist, write DNE.
lim
x2 x 2
x2
b. lim
x2 x 6
x3
c.
5 x 2 19 x
9 x 2 24
a.
x 2
x 3
lim
x
cfw_ 5xx 15
2
2.
Is f (x) =
if x 2
continuous?
Math 144
TR Quiz 1: 9.1
Name:_ Score:_
All answers must follow logically from work provided. You must box your final answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. Place each
Math 144
TR Quiz 2: 9.3 and 9.4
Name:_ Score:_
All answers must follow logically from work provided. You must box your final answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. If
9.2 Practice Quiz
Just for practice. Just for fun!
1) Is the following function continuous?
()
cfw_
2) Is the following function continuous at
?
()
3) Is the following function continuous at
()
?
9.2 Practice Quiz
Just for practice. Just for fun!
4) Find
Math 144
MWF Quiz 3: 9.7 and 9.8
Name:_ Score:_
All answers must follow logically from work provided. You must box your final answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. I
Math 144
TR Quiz 4: 10.1 and 10.2
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your cell phone (or any other
electronic device) any time during the class you will get a zero on this quiz. If you
Practice Quiz: 10.3-10.4
1. [40 points] Find the absolute maxima and minima for
on the given interval.
Write each as an ordered pair.
Absolute Maxima: _ Absolute Minima: _
2. [30 points] If the total cost function for a product is
dollars,
producing how m
Practice Quiz 10.3 and 10.4
1. [40 points] Find the absolute maxima and minima for
on the given interval.
We need to check critical points and endpoints.
Critical values?
Write each as an ordered pair.
Absolute Maxima: _
_ Absolute Minima: _
_
2. [30 poin
Math 144
TR Quiz 5: 10.5
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. If you leave
ea
Math 144
TR Quiz 6: 11.3 and 11.4
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. If you
Math 144
TR Quiz 7: 12.1-12.3
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. If you lea
Math 144
TR Quiz 8: 13.1-13.3
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your cell
phone (or any other electronic device) any time during the class you will get a zero on this quiz. If you lea
Math 144
TR Quiz 9: 13.5 and 13.7
Name:_ Score:_
All answers must follow logically from work provided. You must box each answer. If you use your
cell phone (or any other electronic device) any time during the class you will get a zero on this quiz.
If you
Final Exam Outline
9.1: Limits
o Limits of polynomial functions and limits of rational functions. Can you factor?
9.2: Continuous Functions and Limits at Infinity
o Limits at infinity
9.4-9.6: Derivative Rules
o You must know and be able to use ALL deriva