Problem

Find the Maclaurin series for $ f(x) $ using the …

02:14

Question

Answered step-by-step

Problem 16 Medium Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ 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) = x \cos x $

Video Answer

Solved by verified expert

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 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

Okay, so use definition of Mickler serious to find the metal answers for half of eggs. All right, so ever actually goes to extremes, cousin effects both. And the definition for meth or serious is if we expand it at at zero is gonna be It's absurd to Millie after instructive of zero times X to the in order and Territorial. And we know that the readers committees for effort six and the articles to Billy No. And yet the first purity forever. This is going to be a co site x minus like Site X And second, the rhythm is going to be minus sine X minus esko Xanax and third after the after the vaccine is going be minus coz i x plus x science. So let's can you do it? It's going to do it and find some parents off the driver there. So the affects to the four thirty, but it's going to be minus Plus, Sykes purse looks closer. Yes, All right, so here a phone, there's a pattern. And if you even do the after five, there's going to be co signed. X One is a science which is just equals two with one prime of X. So the pattern ISS, they're right on here. So we fund that so half in FF affects to the river, then it's equals two. The first fourth of max. Yeah, and in this greater or equal to one. So we put in zero. Let's find out what this crunch you're There's gonna be one one zero. It's one and double crew empty is going to be zero minus zero minus ministerial student zero and the third through him. It's going to be minus one. And the fourth there there is going to be zero Okay with one net. So, uh, alright, let's read this. What? We first right on the pants for it with acts zero. So life, the foreign press one for us with three in the back. Uh, affect backs at zero is gonna be one and foreign plus two zero foreign car three zero. It's minus one and four plus four, which is just foreign zero is still zero. All right, so we first raised this out and where you see Do you know for mother for vets, the MacLaurin experience effects to find out what is thie middle answers for X Times Co's on Nets. All right, so here, that's going to be so in. From zero to infinity. Uh, that's the power of foreign cuss one over phone, Cass. When pictorial minus extra poor foreign for three for in that story. Victoria. So that should be the Met Lauren experience of attacks at the point X equals to zero. So let's check this were put in the several terms into it. So when any zeros this isthe one and this is this is three minutes. Zero. Because these two terms is zero and which have the denominator, It's just one and three and one one. Any one is will be five and eight and seven, yet which is which is consistent with here. Okay, so that's the final answer for this question. No.

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.

Problem