Question

cos2x maclarins series

Answer 1

well you will have f(x)= cos2x then you need have f ' and f ''

Answer 2

yes

Answer 3

continue

Answer 4

ok sorry im reading my old calc book and relearning this

Answer 5

the maclaurin series is generated by f. \[\sum_{k=0}^{\infty} (f ^{k}(0)/ k!)x ^{k} = f(0) + f'(0)x + (f''(0)/2!)(x ^{2})+...+...(f ^{n}(0)/n!) x ^{n}\]

Answer 6

yes

Answer 7

continue

Answer 8

did you already have that?

Answer 9

yes

Answer 10

so you want the answer and steps to get there

Answer 11

yes

Answer 12

differential cos2x to get there

Answer 13

f '= -2sin(2x)
f ''=-4cos(2x)

Answer 14

f3 as the next one

Answer 15

f '''= 8sin(2x)
f ''''=16cos(2x)

Answer 16

sin(0)=0
cos(0)= 1

Answer 17

continue

Answer 18

bare with me here im going to type all i have here

Answer 19

-sin(0)= 0
-cos(o)=-1

Answer 20

do cos2x differential it like 5 times

Answer 21

cos(2(0)) -2sin(2(0))x -(4cos(2(0))/2)(x^2)+(8sin(2(0))/3!)(x^3)+(16cos(2(0))/4!)(x^4) -(32sin(2(0))/5!)(x^5)

and i will simplify here in a sec

Answer 22

1-0-2(x^2)+0+16(x^4)+0

Answer 23

you follow me?

Answer 24

yes

Answer 25

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