Notes over Power Series:
Examples:
1)
a) Write out the terms of this power series.
b) Write out the terms of the derivative of this series
c) Write out the terms of the integral of this series.
2) f ( x ) 1 x x 2 x 3 .
a) Write out the sigma notation for
CALCULUS BC
WORKSHEET 1 ON POWER SERIES
1. Derive the Taylor series formula by filling in the blanks below.
Let
f x a0 a1 x c a2 x c a3 x c a4 x c a5 x c . an x c .
2
3
4
5
n
What happens to this series if we let x = c?
f c
so a0
Now differentiate f x t
TO: 2016 AP Calculus BC Students
FROM: T. Ericson, R Garcia, AP Calculus BC Teachers
As you probably know, the students who take AP Calculus AB and pass the
Advanced Placement Test will place out of one semester of college Calculus;
those who take AP Calc
CALCULUS BC
WORKSHEET ON SERIES AND ERROR
Work the following on notebook paper.
1. Let f be a function that has derivatives of all orders on the interval 1, 1 . Assume f 0 1,
1
1
3
f 0 , f 0 , f 0 , and f 4 x 6 for all x in the interval (0, 1).
2
4
8
(a)
Lagrange Form of the Remainder (also called Lagrange Error Bound or Taylors Theorem
Remainder
When a Taylor polynomial is used to approximate a function, we need a way to see how accurately
the polynomial approximates the function.
Taylors Theorem: If a f
More on Error
Alternating Series Remainder
Suppose a series has terms that are alternating, decreasing in magnitude, and having a limit of 0. If the
series has a sum S, then Rn S Sn an1 , where Sn is the nth partial sum of the series.
In other words, if t
CALCULUS BC
POWER SERIES WORKSHEET
Work the following on notebook paper.
1. (a) Find the fourth-degree Taylor polynomial for cos x about x = 0. Then use your polynomial
to approximate the value of cos 0.8, and use Taylors Theorem to determine the accuracy
Taylor Series, Day 2
Ex. Find a Taylor series for each of the following functions by finding derivatives and using the
Taylor formula. Find the first four nonzero terms and the general term.
(a) f x e x 3 centered at x = 3
(b) g x e x 3 centered at x =
Unit 8 Test Review
Due Friday 4/22 for 5 bonus points on your test
Prepare for the test by studying all classroom notes and your own chapter notes
and Identify- who, what, when and why it is important for each of the following
items.
1. McCarthyism
2. Lau
Period 1: 1491-1607 TERMS
Terms
Columbian
exchange
Definition
(include significant dates, places, events,
etc.)
Significance
(why is this person/event/document/concept important?)
Ex. movement of people, goods, plants,
animals, disease and wealth between
I voted Andrew Jackson guilty of all three charges of unlawful removal of Natives,
unwarranted invasion of Florida, and the corruption of the democratic government through the
spoils system.
On the first accusation, it is clear that Jacksons forceful remo
1998-2001- Mayor
of Richmond
2006-2010governor of
Virginia
2009-2011Democratic
Mational
Committee
Chairman
2012- Elected
onto senate
Historical context- September 26, 2016 first presidential debate between
Hillary and Trump and mediated by Lester Holt
FDR eager to have Latin American countries help defend western hemisphere
Good neighbor policy: emphasis on consultation and nonintervention in latin america
Economic influence instead of military force
Appeasing Japan and Germany
US=neutrality
Quarantine
Document 1: Landing of Columbus Engraving
Go to http:/ap.gilderlehrman.org/period/1 and click on Landing of Columbus, 1492 under
Documents then fill in the chart below.
HIPP
Document Analysis
Historical
Context
a painting created 400 years after Columbus
Introduction
Attention Getter
Lyndon B. Johnson the 36th President of United States once said, The vote is the
most powerful instrument ever devised by man for breaking down injustice and destroying the
terrible walls which imprison men because they are d
RHYTHM OF INDIAN
CLASSICAL MUSIC
SNEHAL BHAMARE
PERIOD 1
MR. RICHARDSON
MUSIC OF INDIA
Indian Classical music Indian culture.
Originated from Vedic (Spiritual) ritual chants in the
12th Century from what is now North India, Pakistan,
Bangladesh, Nepal a
Vocabulary Practice 4
1. terse: adj. concise; abrupt
2. volatile: adj. changeable; explosive
3. embellish: v. adorn; ornament
4. piety: n. religious devotion, godliness
5. euphemism: n. a mild expression in place of an unpleasant one
6. eloquence: n. expr
Vocabulary Practice 6
1. rectify: v. set right; correct
2. succinct: adj. brief; terse; to the point
3. listless: adj. lacking in spirit or energy
4. somber: adj. gloomy; depressing; dark; drab
5. reprimand: v. reprove severely; rebuke
6. quandary: n. dil
Vocabulary 7 Practice
Kusta
1. gravity: n. seriousness
2. austere: adj. forbiddingly stern
3. miserly: adj. stingy; mean
4. profane: v. violate; desecrate; treat unworthily
5. expedient: adj. fast; practical
6. deride: v. ridicule; make fun of
7. cryptic:
Key Political Events and
Demographic Trends
1968 - present
I. The Election of 1968
A. Dissension with the Democratic Party
1.The assassination of Robert Kennedy
left the Democratic Party divided between
supporters of Vice President Hubert
Humphrey and Sen
Vocabulary Practice 2
1. gregarious: adj. sociable
2. skeptic: n. doubter; person who suspends judgment until the evidence supporting
a point of view has been examined
3. condone: v. overlook; forgive; excuse
4. innate: adj. inborn
5. satirical: adj. mock
Vocabulary Words
VP1
Name _
Period _
1. commemorate: v. honor the memory of
2. adversary: n. opponent
3. hedonist: n. one who believes that pleasure is the sole aim in life.
4. sycophant: n. servile flatterer; yes-man
5. astute: adj. wise; shrewd; keen
6.
Vocabulary Practice 3
1. pessimism: n. belief that life is basically bad or evil; gloominess
2. precocious: adj. advanced in development
3. ambivalence: n. the state of having contradictory or conflicting emotional
attitudes
4. altruistic: adj. unselfishl
Access Psychology
Hannah Butler
[email protected]
Variables
What did you discover?
Independent variables
"Why is the independent variable labelled
the independent variable? Because it is
independent of research participants'
actions - participants
Name:
.
Chapter 12 Stoichiometry
Solve the following problems:
1.
Determine the mass of lithium hydroxide produced when 0.38g of lithium nitride reacts with water
according to the following equation. (Answer 0.78 g LiOH)
Li3N + 3H2O NH3 + 3LiOH
2.
What ma
Chapter 25
Name_
Assignment one: Read pages 539-549 and answer the following questions
1)
By 1900 how many Americans lived in the cities?
2)
What did the revolution in American agriculture feed?
3)
In what did modern cliff dwellers live?
4)
How did Americ
The Great West and The Agricultural
Revolution 1865-1896
The Clash of Cultures on the Plains
After the Civil War, the Great
West was still relatively untamed,
wild, full of Indians, bison, and
wildlife, and sparsely populated
by a few Mormons and Mexicans