uberathlete
New member
- Joined
- Jan 16, 2006
- Messages
- 48
Hi everyone. I'm having some problems with this question:
Find the Taylor series centered at Pi/4 for f(x) = sinxcosx
What I've done is find derivatives from orders 1 and up and evaluating them with x = Pi/4. I then used these on the general Taylor series formula to get an indication of how the series would look like then I converted it to a form using the summation sign. My answer basically ends up being:
1/2 - sum(from n= 1 to infinity) [(-1)^n * 2^(2n+1)*x^(2n)]/(n!)
I'm not so sure if this is the right answer, and I'm wondering if there's an easier way to to do this without having to manually calculating a whole lot deriveatives.
If anyone could help me out on this it'd be greatly appreciated. Thanks!
Find the Taylor series centered at Pi/4 for f(x) = sinxcosx
What I've done is find derivatives from orders 1 and up and evaluating them with x = Pi/4. I then used these on the general Taylor series formula to get an indication of how the series would look like then I converted it to a form using the summation sign. My answer basically ends up being:
1/2 - sum(from n= 1 to infinity) [(-1)^n * 2^(2n+1)*x^(2n)]/(n!)
I'm not so sure if this is the right answer, and I'm wondering if there's an easier way to to do this without having to manually calculating a whole lot deriveatives.
If anyone could help me out on this it'd be greatly appreciated. Thanks!
