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Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. $ f(x) = \arctan (x^2) $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Idaho State University

Boston College

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.

01:08

Use a Maclaurin series in …

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09:42

okay to find the MacLaurin series for the given function. So at the back Sequels to our attendant of X square Okay, we can consider X Square equals to let's say it takes two t and we can find the takes very warm community. So that is just and from one to infinity t to the power of two minus 1/2, minus one times 91 to power and minus one, which is equal to be just plugging t equals X square. So and still from one to infinity. So this is actually power of four months to over two minutes. One times they want to help them in this one, and the readers of convergence is going to be our equals to one, all right.

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