Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

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) = \ln (1 + x^2) $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\sum_{n=1}^{\infty}(-1)^{n-1} \frac{x^{2 n}}{n}, \quad R=1$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

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.

07:25

Find the Maclaurin series …

16:06

02:17

07:14

02:07

03:03

the problem is finding the McLaren. Siri's half Andi It's radius of religions Graph on its first of beauty Nahmias. Same screen. What do you notice about the relationship between this phenomenal A flood after relax is go to hell in one aspects. Coy. First two behalf on one class acts this They could sum from one to twenty. Thank you. Want the public to minus one hands. Thanks to end over here, then we replace X X square. So we're half after Lex. It's going to help. Long past Exploiter, This is a good song. Want to serenity make you want to The Tower of London Town Sacks to to end Over here there were computers, a radius of emergence Lim and cost Trinity. I have swallowed off. Next. You want extra to have us too. Over Plus one arms and hope for max to two. House nine one one. Which is here too. I scored like this. That's a once over. The readers of convergence is equal to one the original cast and that's it. This graph of the last box divider one is, uh, screw off. How? In one plus x square black wind This one two blue want misty to That's a green one sixty three. We can see that as any increases he and Max becomes, um, fight approximation to the function how in one plus X Y.

View More Answers From This Book

Find Another Textbook