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Use the definition of a Taylor series to find the…

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Problem 7 Medium Difficulty

Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$$ f(x) = \sqrt [3]{x}, \quad a = 8 $$


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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
Grace He
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

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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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, use the definition off a tiller. Siri's by the first of one answer returns over the Siri's for half our backs entered. That's given money off, eh? So first half it is equal to two. The first term it is, too. I have promise he could do one over read hams X to the power off negative to third. So have prom. At this point eight, it's equal to one hams, eight to the power of negative to third, which is equal to third terms. One over four, which is equal to one twelve. It's a second term is one over twelve times X one of ST Second derivative is a one off three times negative to over three, thanks to the public. Negative far over three. I have proof from from pate. It's the heart too negative. Two over nine times, one over already too, which is equal to negative one over three square taps through through the power for so the third term, this one over. Negative one over three. Squire task through to the parlour for you, Holmes to bacterial. How sax months take sport, which is the connective one over three squared, perhaps to into the power X minus. Paid scored Third Dimension as they called you one over three counts negative to over three. I'm selective while off. Three. House Extra negative. Eight over three After from from trumpet, it's a call to ten hour. Three skew comes one over two to the power of it. So close to term. This ten over three skew has won over you in pain. Three. Factorial ex st. It's a problem three.

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Related Topics

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Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Samuel Hannah

University of Nottingham

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.

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