Coordinate Geometry Chapter 5
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Quadratics Chapter 2
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2.
Find the set of values of x for which
x2 7x 18 > 0.
(4)
8.
The equation x2 + 2px + (3p + 4) = 0, where p is
Algebra and Functions Chapter 1
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Calculus Maximus
Notes 1.1: What is AP Calculus?
Chapter 1: What is AP Calculus?
Congratulations on your decision to take AP Calculus. You are now in the elite group (one of
approximately 250,000) of high school students who will be spending many hours ea
Warm Up
Question # 1
Question # 2
Question # 3
Problem Set 23 (#1-4)
Target Goals:
a) Find the average value of a function using the Mean Value Theorem for Integrals
Average Value means y value
How can you find the average y value for the graph below?
Exa
Problem Set # 7: Implicit Differentiation
Introduction
Final Examples
Hand In Problems for Students
Problem Set # 8: Basic Applications of the Derivative
Problem Set # 9
Find the value of c that satisfies the mean value theorem for derivatives. (MVTD)
Fin
UNDERSTANDING THE DEFINITION OF A LIMIT
Definition of a limit:
for the
function f if and only if the following condition
holds: Given any
, there is a
such
that
whenever
.
This means that
1. first you must choose a L which you
think the function f(x) is a
Problem Set # 7: Implicit Differentiation
Introduction
Final Examples
Hand In Problems for Students
Problem Set # 8: Basic Applications of the Derivative
Problem Set # 9
( )
[
(
)
]
Find the value of c that satisfies the mean value theorem for derivatives
Problem Set # 11
When f (x) > 0, ; () < 0, ;
() = 0, point
When f (x) > 0, "concave up"; () < 0,
"concave down" ; () = 0,
Problem Set # 12
Problem Set # 13
Position
Velocity
A
When the velocity if negative, the particle is moving
When the velocity if p
Target Goal: Use shortcuts to help evaluate definite integrals
The Definite Integral
Properties
a.
b.
c.
d.
e.
Given:
Find:
Theorem:
Example
Given:
Evaluate:
Types of Discontinuity
a)
b)
2
y f x
1
0
c)
2
2
1
2
0
y f x
y f x
1
1
1
2
0
1
2
Removable Discontinuity
A
in a graph. That is, a discontinuity that can be "repaired" by filling in a single point. In other
words, a removable discontinuity is a point at
Types of Discontinuity
a)
b)
2
y f x
1
0
c)
2
2
1
2
0
y f x
y f x
1
1
1
2
0
1
2
Removable Discontinuity
A
in a graph. That is, a discontinuity that can be "repaired" by filling in a single point. In other
words, a removable discontinuity is a point at
CalculusProblemSet#3:ThedefinitionoftheDerivative
Themaintoolthatyouwilluseincalculusisthederivative
Youneedtobecomeanexpertatfindingortakingderivatives
Find the slope for the line that passes through the points (3,7) and (8,22)
Now lets take a look at th
Calculus Problem Set # 5:
The product rule
If f(x) = uv, then
The quotient rule
If f(x) =
, then
The Chain rule
If y = f(g(x), then
Calculus Problem Set # 6
:
=
Calculus12:Lesson#1
Graphthefunctionusingyourgraphingcalculatorandtableofvalues
X
Y
Graphthefunctionusingyourgraphingcalculatorandtableofvalues
X
Y
Relationshipbetweenand
Solvethefollowing
Part#2:TrigFunctions
Graphthefunctionusingyourgraphingcalculatoran
Calculus Maximus
Appendix A: Precal stuff to know
Stuff you need to know from Precalculus
Unit Circle
Even and Odd Functions
If f x f ( x) , then f is an even function
If f ( x) f ( x) , then f is an odd functions
Exponents
a 0 1, a 0
Logarithms
ln1 0
a1