Turnandtalk: IEIIII
II"
26. The function f is continuous on the closed interval [0.2] and has values that are given in the table
above. The equation fcfw_x) = must have at least two solutions in t
Ivy Song PD 3
Outline #7
Second Fundamental Theorem of Calculus
x
u
( u )du
d
f ( t ) dt=f
dx a
dx
d
f ( t ) dt=f ( x )
dx a
x
We can define:
f ( x )=f ( a ) + f ' ( x ) dx
a
Trig Limits
lim
0
lim
Li Bing Ivy Song PD 3  Outline #2
Reminder:
Product Rule:
dy
dx
Quotient Rule:
dy
dx
(uv) = uv+vu
(
u
v
)=
v u ' uv '
v2
Chain rule
Equation of a Tangent line and a Normal line to a
curve
Steps:
1. F
Ivy Song Pd 3  Outline #4
Intermediate Value Theorem
o If f(x) is continuous on a closed interval [a, b], then for every d between f(a) and f(b),
there exists a c between a and b so that f(c) = d.
o
Li Bing (Ivy) Song Period 3
AP Calculus AB
Folder #1 10 AP Questions
1) 2012 AP Exam: Multiple Choice Question 5
2) 2012 AP Exam: Multiple Choice Question 9
3) 2008AP Exam: Multiple Choice Question 3
Implicit Differentiation
Find the derivative of a function implicitly by replacing y with
dy
dx
=
dy
dx
Function
Independent Variable
For example:
x2+y2=25
2x+2y*
2y
dy
dx
dy
dx
=0
dy
dx
= 2x
=
2 x
2
Ivy Song PD 3
Outline #8
Review of Inverse Trig
Arcsin(x) = sin1(x)
Arccos(x) = cos1(x)
Arctan(x) = tan1(x)
 Arcsin is a function (every x values has ONE yvalue)
 Arcsin(x)= (+) Q1, Q2
 Arccos(
Ivy Song PD 3
AP Calculus AB
Thanksgiving Assignment Self Analysis
I am currently enjoying AP Calculus AB; its my most challenging math class so far but
the group work and my very competent teacher ma
To nd the volume of a solid of revolution:
3 methods:
1) DiSk Meth0d\ [piggziiiiitszular to the
2) Washer Method/ axis of revolution
3) Shell Method
Use strips parallel
to the axis of revolution
To
Ivy Song PD 3
Outline#9
Differential Equations
dy
Have dx
 Separation of variables
o Manipulate equation so that variables are separated (y and dy on one side  x and
dx on the other side)
o Integra
1. A rectangle has its base on the xaxis and its two upper corners on the parabola
y: 12 x2. What is the largest possible are of the rectangle?
2. An open rectangular box is to be made from a 9 x 1
Ivy Song Pd 3
Outline#6
Dish Method


Strips perpendicular to the axis of revolution
o Vertical Strips: UpperLower  In terms of X
o Horizontal Strips: RightLeft  In terms of Y
ALL STRIPS MUST TO
Ivy Song PD 3
Thanksgiving Assignment
Part I: 15 multiple choice and 3 FRQ
Multiple Choice
1. 1993 MC
2. 1993 MC
3. 1993 MC
4. 1988 MC
5. 1969 MC
6. 1969 MC
7. 1969 MC
8. 1969 MC
9. 1973 MC
10. 1973 M
Ivy Song PD 3  Outline#5
Integration
 antiderivative
EX:
f ( x ) dx=f ( x ) +C
2 xdx=x 2+ c
x is the variable of integration
f(x) is the intergrand
C is the constant of integration
dx is called a
To nd the volume of a solid of revolution:
3 methods:
1) DiSk Meth0d\ [piggziiiiitszular to the
2) Washer Method/ axis of revolution
3) Shell Method
Use strips parallel
to the axis of revolution
To
Li Bing Ivy Song PD 3  Outline #1
Limits
Definition: A limit is the intended height of a function.
In order for the limit to exist:
Lefthand limit must equal the right hand limit.
Limit must be a
Ivy Song Pd 3  Outline #4
Intermediate Value Theorem
o If f(x) is continuous on a closed interval [a, b], then for every d between f(a) and f(b),
there exists a c between a and b so that f(c) = d.
o
Ivy Song PD 3
Outline #7
Second Fundamental Theorem of Calculus
x
u
( u )du
d
f ( t ) dt=f
dx a
dx
d
f ( t ) dt=f ( x )
dx a
x
We can define:
f ( x )=f ( a ) + f ' ( x ) dx
a
Trig Limits
lim
0
lim
Ivy Song PD 3
Outline#9
Differential Equations
dy
Have dx
 Separation of variables
o Manipulate equation so that variables are separated (y and dy on one side  x and
dx on the other side)
o Integra