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Problem

Find a power series representation for the functi…

01:04

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Problem 15 Medium Difficulty

Find a power series representation for the function and determine the radius of convergence.
$ f(x) = \ln (5 - x) $


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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

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Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

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Heather Zimmers

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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

Video Transcript

fun power, serious reputation for function F ax and determine the readers of convergence. Okay, so I'm gonna transport axe into lawn with this pool of five, and it's because against one ministers or five And what this This is long fine, plus lawn one minus X or if I and we're going to spend this part, actually, what is that? So, uh, this is just the integral of when there were one minute six or five the X. So let's have not. Maybe we should modify this by some constant K here, so let's try this. So, what is the Negro Levitt? Is this on long one minus plus to power? That's over five. And I think there is some constant here, so Okay, let's do this. So, what is the relative of long one minus? That's or fight. So this is one hour four, five times, not people one thing. Okay, so we confirmed that the way it goes, Nothing. One fifth. So, uh, yeah, okay. And actually, we could spend this part. So one of our women, this X for fighting is very easy to be expanded into hair Siri's. So this particle becomes to end from zero could be and, uh, extra power in your health. And here I have the differential of reader, the X. So we're gonna integrate this one through the term and actually were able to change the other integral. And the summation in there on his son. So on with the first girl extra card and ORF of love in the X and this summit. And this is just equal to our own life. By my eyes, when you were to the power from past one and some notation Inigo is explored in the eggs. It's rather familiar to us. So on. Okay, let's first you write this part and this is just lawn five minus when there are servants, US one and the integral is gonna be extra power and plus one over and us one. So that's the girl. Yes. Okay, so now we have our results. That's the power of serious reputation for the function for FX on determine the readers of Convergence. So how to find the richest convergence? We gotto push up on it from the step where we just expand dysfunction. So it's this equation we require that that's or fine is from zero ice from the ones who want question, place, axis from knocking fight to five. So that's the rays of convergence, okay?

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Top Calculus 2 / BC Educators
Grace He

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Anna Marie Vagnozzi

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Heather Zimmers

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Joseph Lentino

Boston College

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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Calculate the discriminant of the quadratic expression 2r2 +5x ~2_
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