Problem

Use multiplication of division of power series to…

02:22

Problem 67 Hard Difficulty

Use multiplication of division of power series to find the first three nonzero terms in the Maclaurin series for each function.

$ y = e^{-x^2} \cos x $

Answer

$1-\frac{3 x^{2}}{2}+\frac{25 x^{4}}{24}$

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

So for this problem, we want to use the multiplication of division of power Siri's in order to find the first three, none zero terms in the MacLaurin series. So we're given the function y equals e to the negative X squared coastline X. So we already know that co sign X McLaurin Siri's were given it already in table one. If you want to refer to that and it's negative one to the N of X to the to end time over two n factorial. So with that in mind, we also have e to the negative X squared, Equalling the sum of an equal zero to infinity of negative X squared to the end over in factorial. So with that in mind, another way we could write this would be if we want to rewrite it. We could write it as, um, negative one to the end. Since that's often preferred notation Negative one to the end times X to the two n over n factorial. So that being said, we see that four terms of each will probably be enough. So the first four terms of this will be one minus x squared over two factorial put us back into the boards over four factorial minus X to the sixth over six sectorial. And that obviously keeps going on. But we don't need any more. And then this is gonna be one minus X squared over two factorial plus X to the fourth over two factorial. Um, actually, this will be just X squared, Um, minus X to the sixth over three factorial and then plus go on. So what we'll do is we'll multiply these terms. So what we're gonna end up getting as a result is this right here and then we're gonna multiply this Bye. This right here. So when we do that, what we're gonna end up getting as a result, is simplifying it further. We'll get about one minus X squared over to minus two X squared over two. So these will combine to give us a negative three x squared over two so we can do that right there, and then we'll get plus X to the fourth over 24 plus two x to the fourth over to turning this into 24 will make this into 24. So we'll end up getting 25 x to the fourth over 24 so those would be our first three non zero terms within the MacLaurin series for the specific function.

Problem