Problem

Find the Taylor series for $ f(x) $ centered at t…

02:34

Problem 22 Medium Difficulty

Find the Taylor series for $ f(x) $ centered at the given value of $ a. $ [Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0.$] Also find the associated radius of convergence.

$ f(x) = 1/x,$ $ a = -3 $

Answer

$f(x)=-\sum_{n=0}^{\infty} \frac{(x+3)^{n}}{3^{n+1}} \quad R=3$

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

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

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Video Transcript

The problem is finding the Taylor series for Alfa Back Center that has given value of A and finding associated readers of convergence. So first I have negative three is equal to negative 1/3. A promise is a cultural negative one over expire? Uh huh. From prom is equal to two over x cube and F third derivative. This is a cultural negative three factorial over access to the part of four so we can find that the Earth derivative is equal to negative one to the power of and and times minus one factorial over access to the power of em. Here's a plus one, then f n negative three. It's equally true. Next, the one to the power of end times and minus one factorial over negative three to the power of M s one which is equal to negative and minus one factorial over three to the power of plus one. So the Taylor series for half a wax is some from zero to infinity half and derivative at the point. Negative three over and factorial times X plus three to the power of end, which is equal to some from 0 to 20 Negative one over 10 times three to the power of plus one harms X plus three to the power of the pen. Have a compute limit and go straight. Infinity. Absolute value of make 21 over I'm plus one times ready to power of M plus two over negative one over N times three and plus one, which is equal to the limit, and Austria Final T and over three times and plus one, which is equal to 1/3. So the Raiders of Convergence is equal to 1/1 over three, which is equal to three.

Wen Z.