How Do You Correctly Apply Taylor Series Expansion for f(x-dx)?

[saadsarfraz]

Hi, how would you find the taylor series for f(x-dx). i know that substituting x-dx in the series for f(x) is not correct.

 

[mathman]

You are using an unusual terminology. Typically a Taylor series looks like:

f(a+x)=f(a) + xf'(a) + x² f''(a)/2! + ...

When a=0, it is called a MacLaurin series.

 

[saadsarfraz]

what happens if you have dx instead of a. the second post on this website http://www.wilmott.com/messageview.cfm?catid=19&threadid=17563
has a formula but i don't know how it was derived.

 

[raymo39]

u are using dx in the sense of a second point of x, or a change in x
check out this page from wikiversity that breaks everything down really well.
normally i know that posts from wiki are frowned upon, but i learned from this site and i think they break it down really rigorously and guide you nicely through the expansion of a function into a summed power series and then into taylors series at different points.
http://en.wikiversity.org/wiki/Taylor's_series

 

[elibj123]

Saying "Taylor Series" is not enough, you have to attach a point around which you are expanding the function. Notice that around a different point, the taylor series will also have different coefficients.

In your example, f(x+dx) was calculated around a point x, so of course substitution won't work for the exapnasion of f(x) around 0.