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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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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Oregon State University

University of Nottingham

Lectures

01:59

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.

02:28

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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Use the definition of a Ta…

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Find the Taylor series of …

01:18

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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