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Problem

Find the Maclaurin series of $ f $ (by any method…
02:34

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Problem 45 Medium Difficulty

Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $

$ f(x) = \cos (x^2) $

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Related Courses

Calculus 2 / BC
Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Related Topics

Sequences

Series

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Top Calculus 2 / BC Educators
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Anna Marie Vagnozzi

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Lectures

Video Thumbnail

01:59
Series - Intro

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.
Video Thumbnail

02:28
Sequences - Intro

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.
Join Course
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Watch More Solved Questions in Chapter 11

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

the problem is finding Michael Oren. Siri's off off on this really is burdens Graff half on DH. It's rest of futile Oprah Nahmias on the same screen. What do you notice about a relationship in this half? Half of axe is equal to assign X koi supposed to have signed X if they caught you some from zero to infinity If you want to end times X to Teo over to end Vittorio then we replace acts by ex Squires We've got a flex. This is Nico saw from zero to twenty. Next you want and hams Axe too foreign over to end. I love you. There were computers, a radius of convergence Damn it and crossed the infinity. Absolutely. Oh, ax to four end or over to him Last two factorial times. Yeah, two in fact, Arial over tax to foreign. This is a limit cost Trinity I just for over two possible one halves to, uh, pass too, which is equal to zero. The readers of convergence is going to be fine. That's little cat. It's graphs. Zariah curve is have a lax green one. This is zero. The blue one. This she wants on our angel Juan is too notice that, as in increases, he index becomes a biting approximation to the function Kasai X Square.

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Related Topics

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Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:59
Series - Intro

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.
Video Thumbnail

02:28
Sequences - Intro

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.
Join Course
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