Geometry 9H
Chapter 13 Summary (Coordinate Geometry)
13.1 Distance Formula
This section teaches about the distance formula. The distance formula is: = Distance. Also, there is the
circle formula: = Radius.
13.2 Slope of a Line
This section is about the sl
Pg: 71, Problem # R0
8/31/2012
Topic: Limit, derivative, definite integrals, continuity, intermediate value theorem.
The most important things I learned in chapter 2 are continuity and infinite limits.
Continuity is basically the ideology of whether or no
Pg: 79, Problem # 9
9/5/2012
Topic: Derivative.
As a result of doing this problem (the Spaceship Problem), I learned that derivative is
defined as the instantaneous rate of change of a function, but physically it portrays the slope of
the line tangent to
Pg: 141, Problem # 33
10/2/2012
Topic: Product Rule and Quotient Rule of Derivatives.
The two most important things I have learned are from section 4.2 and 4.3: the product
rule and the quotient rule of derivatives. I learned that when it is necessary to
Pg: 183, Problem # 17e
10/16/2012
Topic: Constant of Integration, C.
The constant of integration, C, basically states the yintercept of the graph. This arbitrary
constant is basically responsible for the vertical shift of a graph from its general locatio
Pg: 262, Problem # 61
11/07/2012
Topic: Fundamental Theorem of Calculus Derivative of an Integral Form.
Since my last journal entry, the most important thing I learned is another fundamental
theorem that lets you find the derivative of an integral without
Pg: 338, Problem # 9
01/14/2013
Topic: Euler's Method.
Since my last journal entry, one of the most important things I learned is the Euler's
method in calculus. Euler's method provides a nearly accurate method of graph a function on a
slope field. Withou
Pg: 369, Problem # 44
01/24/2013
Topic: Second Derivative and Concavity.
Since my last journal entry, one of the most important things I learned is the analysis of second
derivative and its relationship with the original graph. I learned beforehand that f
Pg: 427, Problem # R0
02/11/2013
Topic: 3D Solid Figure created by revolving a Plane Figure  Disk, Washer, Shell Methods
Since my last journal entry, most important concept I learned are the three procedures of finding
the volume of threedimensional sol
Pg: 52, Problem # 25
8/23/2012
Topic: Definition of Limit.
I learned a new method of stating the definition of limits using shortened notations:
L = iff > 0 > 0 if 0 < x c < => f(x) L <
The new method helped me write out the definition very quickly,
Topic: Limit, Derivative, Definite Integral.
During the first couple of days in calculus, I was inclined to learn the definition of limit:
L is the limit of f(x) as x approaches c
If and only if
For any positive number epsilon, no matter how small,
There
Geometry 9H
Chapter 1 Summary
1.1 Points, Lines, Planes, Angles
This section is about points, lines, planes, and angles. The main concept of this
section is equidistant. Example, point A is a cm. right from point O and point B is a
cm. left from point O;
Fibonacci
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Hello everyone. Wassup! My name is Arko. I'm a
Using TI83/84 CALCULATE
functions
Calc BC Review Material
(primarily Chapters 110)
AP Calculus BC
References are from AP Calc 2003 BC Exam, Parts A & B
Unit Circle: (x,y) = (cos, sin)
Must know trig functions of common angles!
Make sure you practice wi
Arko Dewri
Period 1
AP Calculus BC
4/29/2013
26 steps to a 5 (write ups) # 2
a. Find the speed of a particle?
Speed of a regular function = or
Speed of a parametric function = or
For example, find the speed from the equations x(t) = and y(t) = 2t at t = 1
Arko Dewri
Period 1
AP Calculus BC
4/22/2013
26 steps to a 5 (write ups)
g. Write a Taylor Polynomial?
P(x) = f(a) + f '(a)(x a) + f '(a)(x a / 2! + . + (a)(x a / n! + .
Let a = 0 and f(x) = cos x
So, f '(x) = sin x
f '(x) = cos x
P(x) = cos 0 sin 0 (x 0
Definitions and Theorems:
Limit: L is the limit of f(x) as x approaches c if and only if for any positive number
epsilon, no matter how small, there is a positive number delta, such that if x is within
delta units of c, but not equal to c, then f(x) is wi
Calculus Cheat Sheet
Limits
Definitions
Precise Definition : We say lim f ( x ) = L if
Limit at Infinity : We say lim f ( x ) = L if we
x a
x
for every e > 0 there is a d > 0 such that
whenever 0 < x  a < d then f ( x )  L < e .
can make f ( x ) as clo
Pg: 492, Problem # 28
02/22/2013
Topic: Improper Integrals.
Since my last journal entry, one of the most important things I learned is the method for solving
improper integrals. There are three types of improper integrals: one that goes from a constant to
Arko Dewri
Period 1
AP Calculus
840 East Citrus Avenue (Room 405)
Redlands, CA 92374
December 10, 2012
Dear Future Student of Calculus,
I am writing to let you know all about my understanding about this new class you are
going to take, about what you will
Common Derivatives And Integrals
Integral Rules
Derivative Rules
d
(sin u)
dx
=
cos u
du
dx
Z
sin u du
= cos u + C
d
(cos u)
dx
= sin u
du
dx
Z
cos u du
=
d
(tan u)
dx
=
Z
tan u du
= ln j cos uj + C
d
(csc u)
dx
= csc u cot u
du
dx
Z
csc u du
= ln j csc u
Andrew Rosen
Average Value of a Function:
()
Inverse Trig Function Derivatives:
y = Arcsinu
y =
y = Arccosu
y =
y = Arctanu
y =
y = Arccotu
y =
y = Arcsecu
y =
y = Arccscu
y =
 
 
Inverse Trig Function Integrals: (use when you dont have what you need)
Andrew Rosen
RAMs:
LRAM (height is on left side): (
)
RRAM (height is on the right side): (
MRAM (height is in the middle): (
Trap: (
)
)
)
Volume:
Perpendicular to x axis:
( )
Perpendicular to y axis:
( )
Area of equilateral triangle:
The side is alway
Andrew Rosen
Mean Value Theorem: If f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a point , c,
in (a, b) such that f(c) =
()
()
Rolles Theorem: A differentiable function with equal value
Andrew Rosen
Geometric Series:
If r < 1: Series converges
If r < 1: Series Diverges
Sum of finite:
Sum of infinite:
Theorems for Infinite Series:
1) If the sequence does not converge to 0, then the series diverges (do the limit via lHopital)
a. If th
Andrew Rosen
Trig Identities:
sec x =
tan x =
csc x =
cot x =
2
2
2
2
sin x + cos x = 1
cot x +1 = csc x
tan2x +1 = sec2x
sin 2x = 2sinxcos x
cos 2x = 12sin2x
cos (A+B) = cos A cos B sin A sin B
cos (AB) = cos A cos B + sin A sin B
sin (A+B) = sin A cos
Andrew Rosen
Trig Identities:
sec x =
tan x =
csc x =
2
2
sin x + cos x = 1
sin 2x = 2sin x cos x
cos (A+B) = cos A cos B sin A sin B
cos (AB) = cos A cos B + sin A sin B
sin (A+B) = sin A cos B + cos A sin B
sin (AB) = sin A cos B cos A sin B
cot2x +1
Andrew Rosen
Taylor Series:

( )
(
)
Maclaurin is when c=0
Lagrange Error:
(
( )

)

( ) is equivalent to the maximum
o The maximum can be found if it is a trig function and has a natural maximum that is
apparent
o The maximum can be found by going to