Home
Explore
Exams
Search for anything
Login
Get started
Home
Calculus Unit 10
Calculus Unit 10
0.0
(0)
Rate it
Studied by 1 person
View linked note
Learn
Practice Test
Spaced Repetition
Match
Flashcards
Card Sorting
1/19
There's no tags or description
Looks like no tags are added yet.
Study Analytics
All
Learn
Practice Test
Matching
Spaced Repetition
Name
Mastery
Learn
Test
Matching
Spaced
No study sessions yet.
20 Terms
View all (20)
Star these 20
1
New cards
Series
What do you call an expression of the form a1+a2+a3+⋯+an+…?
2
New cards
Terms of a Series
In the series a1+a2+a3+… what are the individual elements a1, a2, a3,… called?
3
New cards
Partial Sum
For a series ∑n=1∞an, what is the sum Sn=a1+a2+⋯+an known as?
4
New cards
Sum of a Series
If the sequence of partial sums Sn converges to a limit S, then S is called the ______ of the series.
5
New cards
Convergent Series
A series is called ______ if its sequence of partial sums converges.
6
New cards
Divergent Series
A series is called ______ if its sequence of partial sums does not converge.
7
New cards
Geometric Series
What do you call a series of the form a+ar+ar2+⋯+arn−1+…?
8
New cards
Common Ratio
In a geometric series a+ar+ar2+…, what is the value r called?
9
New cards
Convergence of a Geometric Series
A geometric series with ratio r converges if ______ and its sum is ______.
10
New cards
Power Series
What do you call a series of the form ∑n=0∞cn(x−a)n=c0+c1(x−a)+c2(x−a)2+…?
11
New cards
Radius of Convergence
For a power series, what is the number R≥0 such that the series converges for |x−a|
R called?
12
New cards
Interval of Convergence
What do you call the set of x-values for which a power series converges?
13
New cards
Taylor Series
If a function f has derivatives of all orders at x=a, then the series ∑n=0∞f(n)(a)n!(x−a)n is called the ______ series of f at a.
14
New cards
Maclaurin Series
What is the Taylor series of a function f centered at a=0 called?
15
New cards
Taylor Polynomial of Order n at a
What do you call the polynomial Pn(x)=f(a)+f′(a)(x−a)+f′′(a)2!(x−a)2+⋯+f(n)(a)n!(x−a)n that approximates f(x) near x=a?
16
New cards
Remainder of Order n (Taylor’s Formula)
If f(x)=Pn(x)+Rn(x), then Rn(x) is called the ______.
17
New cards
Taylor’s Theorem with Remainder
State the formula that expresses the remainder Rn(x) in terms of an integral or a derivative evaluated at an unknown point.
18
New cards
Telescoping Series
What type of series is one where most terms cancel out in the partial sums, leaving only a fixed number of terms?
19
New cards
Alternating Series Test
What test can be used to determine the convergence of a series whose terms alternate in sign?
20
New cards
Absolute Convergence
A series ∑an converges ______ if the series of absolute values ∑|an| converges.
Explore top notes
Chapter 6 - Motivation concepts
Updated 1017d ago
Note
Preview
Chp 14: Organizing Your Presentation
Updated 847d ago
Note
Preview
Diagnosing Psychological Disorders
Updated 949d ago
Note
Preview
Ecology: Communitiy
Updated 1001d ago
Note
Preview
Chapter 4 - The Energy of Life
Updated 793d ago
Note
Preview
Chapter 4: Travel and tourism products and services
Updated 963d ago
Note
Preview
IB History: Paper 1 - The Move To Global War (Japanese, Italian and German Expansion)
Updated 254d ago
Note
Preview
HSK4 Adjectives Part 2/3
Updated 146d ago
Note
Preview
Explore top flashcards
PD E3 - Trauma
Updated 3d ago
Flashcards (69)
Preview
Viet 4 Chapter 8 Lesson 1
Updated 571d ago
Flashcards (40)
Preview
Cleopatra revision
Updated 774d ago
Flashcards (50)
Preview
Cooking
Updated 725d ago
Flashcards (41)
Preview
last spanish quiz
Updated 356d ago
Flashcards (24)
Preview
Latin America Study Guide
Updated 813d ago
Flashcards (63)
Preview
Written automotive
Updated 597d ago
Flashcards (33)
Preview
Unit 5: Conflict, Crisis, and Reaction in the Late 18th Century
Updated 760d ago
Flashcards (54)
Preview