Hello!
I need help figuring out the Taylor series..I keep getting undetermined form in these functions..Please help!
Q1) Suppose f(x) = cos(2x) is replaced by its Taylor Polynomial P2(X) about the point X(0) = pi/2 on the interval 0<= x <= pi. Estimate the error?
Q2) Derive the Taylor Series for f(x) = ln(1+x) with X(0) = 0 and determine for which value of X the series converges.
Thanks!
Edit: sorry, ignore this, didn't see mathstud's post
The formula you are probably using isQ1) Suppose f(x) = cos(2x) is replaced by its Taylor Polynomial P2(X) about the point X(0) = pi/2 on the interval 0<= x <= pi. Estimate the error?
where M is the maximum value of on the interval and r is the maximum distance from the point around which the taylor series is expanded and a point in the interval.
If this doesn't make sense I don't know how you are supposed to do this, but I am sure there is a way.Q2) Derive the Taylor Series for f(x) = ln(1+x) with X(0) = 0 and determine for which value of X the series converges.
using geometric series, with |-x|<1
The series converges whenever |x|<1 because 1 is the distance to the nearest value of x that produces a singularity in C.
I dunno. I'm a second year student at Melbourne uni and I don't recall having seen it. The most advanced stuff I have done in power series was in a semester of complex analysis, although Taylor series have been a major part of every single subject I have done since starting uni except my first year programming subjects. I also learn stuff as I read on this forum, which gives me a more patchy education on certain topics, but that doesn't really apply to power series because I have been doing that as part of my course.How is it that you are working with power series but are ignorant of the Root test (not at all meant to be hostile, I am just curious)
Hmm, that is interesting. You have taken complex analysis, with all its Laurent series and such I am sure then that you are well aquainted with poewr series, but usually the Root test which is an integral part of series convergence/divergence you skipped. It's not a bad thing I suppose, just peculiar . You should probably learn it