Question

Taylor series

What is the taylor series of f(x) = cos(x^2)? As I recall, my prof said that we should replace the x in the taylor series with x^2 so it's 1- (y^2)/2! + (y^4)/4! +....
How is it that we can get the taylor series without a certain point? Can someone please explain this to me?

Answer 1

I think you mean to replace the x^2 with y

Answer 2

and it seems that it has been implicitly assumed here to be about x=0

Answer 3

so far you have it right if you replace x^2 with y

Answer 4

I still don't get it.. how come we have a variable, x, instead of cos or sin in the taylor series?

Answer 5

do you know the definition of the Taylor series?

Answer 6

and since x=0, shouldn't the answer be 0? :S

Answer 7

Yes, I looked it up

Answer 8

I don't think you quite grasp Taylor series...

Answer 9

one sec...

Answer 10

the Taylor series about x=a is given by\[f(x)=\sum_{n=0}^\infty{f^{(n)}(a)\over n!}(x-a)^n\]what is a in this case?

Answer 11

0. Oh, I realized I forgot the latter part of the taylor series, (x-a)^n

Answer 12

since the derivative of cos(x) is -sin(x), I guess every (2n+1)th derivative is a 0?

Answer 13

exactly :)

Answer 14

good job, it looks like you only needed a little tip