3 items are filed under this topic.








The Maclaurin series generated by f(x)=x^ cosx + 1 
20050810 

From Latto: f(x)=x^{3}·cosx + 1. but when I take the derivatives, I couldn't see a pattern. Can you help?
Answered by Penny Nom. 





A Taylor series 
20010427 

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 
20000923 

From Jason Rasmussen: I suppose my confusion comes into play when I am trying to figure out where the x^{n} term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ br^{n} ] where the limit is b/(1r) for convergence at  r  <1. Therefore, the function f(x) needs to somehow take the form of b/(1(xa)), which may take some manipulation, and by setting r = (xa) and b = C_{n}, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives C_{n} = f^{n}(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = e^{x} take the form of f(x) = b/(1(xa)). 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 [f^{n}(a) * (xa)^{n} / n!]? Answered by Harley Weston. 


