Finding the Maximum Remainder in a Taylor Series: Explained

[Skrew]

Hello, I was wondering if anyone could explain to me the thought process behind how you find the maximum remainder of a Taylor series?

I read the wiki article and didn't help me at all,

http://en.wikipedia.org/wiki/Taylor's_theorem

My book talks about something like this(image is wiki's):

but I don't understand how its derived or what it really means.

Thanks for any help.

 

[Metahominid]

We never really did too much with this, however in Taylor polynomials you are generating an approximation through a polynomial. How accurate you are is dependent upon how many time you can differentiate the function and what value you choose for the function. The polynomial approximates the function as the order, n, approaches infinity however computing this isn't really possible so when you are trying to find the value of a function at point you really are asking yourself how accurate do you wish to be. By adjusting n in the inequality you can attempt to increase accuracy. This is important for engineering and other experts when they demand a certain tolerance of error.

 

[bignum]

Basically that fancy equation tells you the term after your last time is your error.