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WOLFRAM|DEMONSTRATIONS PROJECT

Quality of Approximation by Geometric Series

0.8

polynomial degree

f(0.800) = 5.0000000

p(0.800) = 1.0000000

error = | f(0.800) - p(0.800) |

= 4.000

p(x) = 1

This Demonstration shows graphically and numerically the quality of approximating the function values of

f(x)=

1-x

for any

x∈(-1,1)

by the Taylor polynomial

p(x)=1+x+

+...+

, where

n=0,1,2,…,50

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