Associated Topics || Dr. Math Home || Search Dr. Math

### Taylor Series (Calculus II)

```
Date: 2/14/96 at 18:57:10
From: Anonymous
Subject: Taylor Series (Calculus II)

I don't have a real specific question. I am having difficulty
understanding the Taylor Series and Maclauren Series. I guess I am
having trouble with all areas of the Thomas, Finney 8th edition
Calculus textbook's eighth chapter.

I was looking for some help on the theory behind the error estimate
and "c" in particular - I am not understanding it. I am looking for a
really super guide that would help me better understand Calc II and
where I might get this. My professor just does examples and doesn't
explain the theory.

Thank you very much. I'm sure you won't know how much I appreciate
this.
```

```
Date: 7/29/96 at 13:41:47
From: Doctor Jerry
Subject: Re: Taylor Series (Calculus II)

The c in the Mean-value Theorem

f(b)-f(a)=f'(c)(b-a)

is a point between a and b, which (for smooth functions) is known to
exist but is not necessarily easy to calculate.  Geometrically, it's
quite clear that there must be a value of x, call it c, between a and
b for which the slope of the line joining (a,f(a)) and (b,f(b)) is
exactly equal to the slope of the graph of f at (x,f(x)).

The c in Maclaurin's formula   f(a+h) =
f(a)+f'(a)x/1!+f''(a)x^2/2!+...+fn'(a)x^n/n!+fn+1'(c)x^(n+1)/(n+1)!
where fn' means the nth derivative and fn+1' means the (n+1)st
derivative, is precisely analogous to the c in the Mean-value Theorem.

The proof that it exists is more complicated, but not different in
kind.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search