# taylor series problem - find error bound interval

• Apr 4th 2008, 01:36 PM
juntheking@yahoo.com
taylor series problem - find error bound interval
Basically I have to find the interval based at b = 1 for the function f(x) = ln(x) with an error bound at most 0.01 for the first Taylor polynomial (n = 1). I know how to do it with an interval given, but am lost with this "twist" of not having a bound.

Thank you
• Apr 5th 2008, 12:33 AM
Opalg
Quote:

Originally Posted by juntheking@yahoo.com
Basically I have to find the interval based at b = 1 for the function f(x) = ln(x) with an error bound at most 0.01. I know how to do it with an interval given, but am lost with this "twist" of not having a bound.

You have a formula for the error (or remainder) after n terms, and you have to choose the length of the interval so as to ensure that this error is less than 0.01. But you can't do that unless you know the value of n. Unless the question indicates how many terms of the Taylor series are to be used, I don't see how you can answer the question.
• Apr 5th 2008, 08:07 AM
juntheking@yahoo.com
OH! I'm sorry I left that vital piece of information out. The nth term is 1. I will fix my original post also.

THanks