An improvement to the Polygonal Method:
Consider segment PR, joining two consecutive points in the original approximation. Find y' at the midpoint Q of PR. Draw a line through P with this slope, and mark off an improved approximation R' to replace R. This is equivalent to using the third term (second derivative) in the Taylor series expansion. _____________________________ Polygonal Approximation: 1. Step-by-step construction [url]http://www.geogebratube.org/material/show/id/27865[/url] 2. Transfer the procedure to the Spreadsheet view: [url]http://www.geogebratube.org/material/show/id/27754[/url] *[b]3. Improvement: Add a term in the Taylor expansion[/b]* 4. Comparison, and corrector formulas: [url]http://www.geogebratube.org/material/show/id/29107[/url]