# Thread: Remainder and Error of Taylor Series

1. ## Remainder and Error of Taylor Series

Estimate ln(0.3) by using S10 for the Taylor series for lnx. Approximately what does the remainder of the series equal for this value of x? Is the absolute value of this remainder an upper bound for the absolute value of the error in approximating ln(0.3) by S10(0.3)?

2. ## Re: Remainder and Error of Taylor Series

Hey citcat.

As I recall, you can have the error bound of a Taylor series approximation that is based on the nth derivative. Here is the idea (its called the Lagrange Error Bound):

http://clem.mscd.edu/~talmanl/PDFs/A...s/Lagrange.pdf