The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages. 
Home Infinite Series Taylor's Formula Examples Example 2: MacLaurin's Formula  
Search the VIAS Library  Index  
Example 2: MacLaurin's Formula
Find MacLaurin's Formula for f(x) = e^{x}. The nth derivative is f^{(n)}(x) = e^{x }f^{(n)}(0) = 1. MacLaurin's Formula is for some t_{n} between 0 and x. For t between 0 and x the value of e^{t} is always less than or equal to 3^{x}, for e^{t} ≤ e^{x} ≤ 3^{x}. We therefore have the formula (3) , The formula (3) can be used to approximate e^{x}. Let us set x = 1 and approximate e. The error estimate is now
This compares with e = 2.718282.


Home Infinite Series Taylor's Formula Examples Example 2: MacLaurin's Formula 