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taylor series

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Infinite Logarithmic Series 2011-08-08
From Sourik:
Dear Expert,

In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between -1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof.
Thanking you,
Sourik

Answered by Robert Dawson.
A Taylor polynomial for (lnx)/x 2010-09-29
From Dave:
I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, -3, 11, -50, 274... Ok, so the negative is an easy fix -> (-1)^n-1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this? Thanks!
Answered by Chris Fisher.
The Maclaurin series generated by f(x)=x^ cosx + 1 2005-08-10
From Latto:
f(x)=x3cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
Answered by Penny Nom.
A Taylor series for ln(x) 2005-04-16
From Anood:
i have to represent ln(x) as a power series about 2

i`m not getting the final answer which is ln 2+ sigma (((-1)(n+1)/ (n*2n))*(x-2)n). i don`t get the ln 2 part

i show you my trial

f(x)= ln x.

f-(x)=(1/x) .

f--(x)= (-1/x2)*1/2!

f---(x)= (2/x3)*1/3!

f----(x)= (-6/x4)* 1/4!

so the pattern shows me that f(n)= ((-1)(n+1))/xn *n)

so f(2)= sigma ((-1)(n+1))/2n *n) *(x-2)n

so as you see i don`t get ln 2


Answered by Penny Nom.
The third derivative 2004-10-15
From Holly:
Why would you ever take the third derivative?
Answered by Harley Weston.
Programming without trig functions 2004-05-25
From Derek:
I am a programmer trying to calculate the following.

What is the formula to find the cross-sectional area of a cylinder with out using any trig functions? or better yet, how can you calculate any given volume in a cylindrical tank with spherical heads with out trig functions?

I am using a PLC (programmable logic controller) to do this and trig functions are not available.

Answered by Harley Weston.
Cosine of 35 degrees 2004-03-03
From Jason:
How do you find the exact solution to cosine 35 degrees.
Answered by Chris Fisher.
A Taylor series 2001-04-27
From Karan:
Given the following information of the function
  1. f''(x) = 2f(x) for every value of x

  2. f(0) = 1

  3. f(0) = 0
what is the complete Taylor series for f(x) at a = 0

Answered by Harley Weston.
Maclaurin series again 2000-09-23
From Jason Rasmussen:
I suppose my confusion comes into play when I am trying to figure out where the xn term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ brn ] where the limit is b/(1-r) for convergence at | r | <1. Therefore, the function f(x) needs to somehow take the form of b/(1-(x-a)), which may take some manipulation, and by setting r = (x-a) and b = Cn, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives Cn = fn(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = ex take the form of f(x) = b/(1-(x-a)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [fn(a) * (x-a)n / n!]?
Answered by Harley Weston.
 
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