Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

(a) Use differentiation to find a power series re…

08:46

Question

Answered step-by-step

Problem 12 Medium Difficulty

Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence.
$ f(x) = \frac {2x + 3}{x^2 + 3x + 2} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Yiming Zhang
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Yiming Zhang

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Related Topics

Sequences

Series

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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
Recommended Videos

04:10

Express the function as th…

0:00

Express the function as th…

02:38

Express the function as th…

04:50

Express the function as th…

09:44

$11-12$ Express the functi…

03:25

$11-12$ Express the functi…

02:47

$11-12$ Express the functi…

02:22

$11-12$ Express the functi…

13:23

$11-12$ Express the functi…

12:47

$11-12$ Express the functi…

02:15

$11-12$ Express the functi…

01:18

Find a power series repres…

02:11

Find a power series repres…

01:39

$11-12$ Express the functi…

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

Video Transcript

okay. So expressive function as a sum of power, serious by first using partial fractions and find the in the role of convergence. So that bag's equals to ask for three times. So we're going to fetter out this part, It becomes at plus one times. This was too one over it. And this is just so it's a difference of two factions when investment plus one minus one or restless too. Yeah, and, ah, we can expand this part from that firm. And it just not wanted power in extra power and from zero to infinity minus. So actually, we're here. We're gonna hold out to here. So becomes one of us. Have bags end. This is just what happy soul here, minus one two hour in extra oven, over to help it. And from zero to infinity. I know him. I might as well just But it's who inside it. So this is to empower us one, and yeah, this is help. Our serious and Phil can simplify it. Bye. Plus tax insurance, the's some, but okay, we can wield it as an alternative form. So this is the same one. But if you want to know that we can destroy it. Extroverted plus one minus. If you're dating like you want our end acts to power. Plus one answered about this one. So this is the to ask past this part which is right here a parenthesis here. And the three comes this part. Here, have this that you want a part in that of an over tubes of this one. Done and find the interval burdens so we can fund it from here. Think, Creon one. So s the absolutely fattest, less than one end two over axe. That's over to the absolutely the absolute Oh, that's over, too. Is less than one wishing kleiss the interval convergence I because a two one, two, one. Okay.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
95
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Kristen Karbon

University of Michigan - Ann Arbor

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

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
Recommended Videos

04:10

Express the function as the sum of a power series by first using partial fracti…

0:00

Express the function as the sum of a power series by first using partial fracti…

02:38

Express the function as the sum of a power series by first using partial fracti…

04:50

Express the function as the sum of a power series by first using partial fracti…

09:44

$11-12$ Express the function as the sum of a power series by first using parti…

03:25

$11-12$ Express the function as the sum of a power series by first using partia…

02:47

$11-12$ Express the function as the sum of a power series by first using partia…

02:22

$11-12$ Express the function as the sum of a power series by first using partia…

13:23

$11-12$ Express the function as the sum of a power series by first using parti…

12:47

$11-12$ Express the function as the sum of a power series by first using parti…

02:15

$11-12$ Express the function as the sum of a power series by first using partia…

01:18

Find a power series representation for the function and determine the interval …

02:11

Find a power series representation for the function and detemine the interval o…

01:39

$11-12$ Express the function as the sum of a power series by first using partia…
Additional Mathematics Questions

02:05

18. A computer password consists of four letters (A through Z) foll…

00:01

A certain brand of automobile tire has mean life span of 35,000 mil…

00:01

A certain brand of automobile tire has mean life span of 35,000 mil…

00:01

The marks obtained in statistics in a certain examination found to …

00:01

The marks obtained in statistics in a certain examination found to …

05:35

An aircralt (at Z) is spotted by two observers (at X and Y) who are…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started