The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: [ap-calculus] Re: Help BC 1997 #24
Replies: 1   Last Post: Apr 15, 2004 9:17 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Richard J Maher

Posts: 80
Registered: 12/6/04
[ap-calculus] Re: Help BC 1997 #24
Posted: Apr 15, 2004 9:17 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Hello Art,

Given the Taylor Series for sin(x), the series for sin(x^2) is
x^2 -x^6/3! + x^10/5! + .... Since sin(x) equals its Taylor
Series on it interval of convergence, which is all of R,
so too f'(x) = sin(x^2) = x^2 -x^6/3! + x^10/5! + ... on R.
(This essentially is composition of functions.) When you integrate
you get f(x) = x^3/3 - x^7/(7*(3!)) + x^11/(11*(5!)) + ...
Hence the -1/42 appears as the coefficient for x^7.

Hope this helps.

Dick Maher

Richard J. Maher
Mathematics and Statistics
Loyola University Chicago
6525 N. Sheridan Rd.
Chicago, Illinois 60626

On Wed, 14 Apr 2004, Art Stahl wrote:

The Taylor series for sin x about x = 0 is x - x^3/3! + x^5/5! -
... If f is a function such that f '(x)=sin(x^2) then the
coefficient of x^7 in the Taylor series for f (x) about x = 0 is

a) 1/7! b) 1/7 c) 0 d) -1/42 (correct answer) e)
I got the answer but my solution is verrrrrry long. I took the 7th
derivative (6th past f ') and evaluated it at at x = 0 and divided by
7!.. It worked!!


Art Stahl

You are subscribed to ap-calculus as:

To unsubscribe send a blank email to

To update your preferences, search the archives or post messages online, visit

If you need help using Lyris web interface go to:

Visit AP Central(tm) - The online resource for teachers, schools, colleges, and education professionals--

The College Board
45 Columbus Avenue
New York, NY 10023-6992

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.