• Support PF! Buy your school textbooks, materials and every day products Here!

Taylor Series Problem

  • #1
26
3

Homework Statement



Let f(x)=cos(x^5). By considering the Taylor series for f around 0, compute f^(90)(0).
by the way, I don't know how super/sub script works?

Homework Equations




The Attempt at a Solution


I tried to substitute x^5 into x's Tyler Series form and solve for f^(90)(0), but it gave me a wrong answer.
 

Answers and Replies

  • #2
33,270
4,975

Homework Statement



Let f(x)=cos(x^5). By considering the Taylor series for f around 0, compute f^(90)(0).
by the way, I don't know how super/sub script works?

Homework Equations




The Attempt at a Solution


I tried to substitute x^5 into x's Taylor Series form and solve for f^(90)(0), but it gave me a wrong answer.
Show us what you got when you did the substitution. That's the right approach.

BTW, it's Taylor series, not Tyler series.
 
  • #3
26
3
cosx=∑(-1)^n/(2n)!*x^2n
I am not sure what the an part: (-1)^n/(2n)! will becomes when I substitute x5 into the series.
 
  • #4
33,270
4,975
cosx=∑(-1)^n/(2n)!*x^2n
I am not sure what the an part: (-1)^n/(2n)! will becomes when I substitute x5 into the series.
Nothing changes in that part. In your formula above, replace x by x5. That will be your Taylor series for cos(x5).

It might be helpful to write the new series in expanded form rather than in closed form (as a summation).
 

Related Threads on Taylor Series Problem

  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
966
  • Last Post
Replies
3
Views
927
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
20
Views
9K
  • Last Post
Replies
4
Views
14K
  • Last Post
Replies
6
Views
7K
  • Last Post
Replies
1
Views
527
Top