  Math Central - mathcentral.uregina.ca  Quandaries & Queries    Q & Q    Topic: taylor series   start over

9 items are filed under this topic.    Page1/1            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, SourikAnswered 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)=x3·cosx + 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 f''(x) = 2f(x) for every value of x f(0) = 1 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.      Page1/1    Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.    about math central :: site map :: links :: notre site français