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Quality of Approximation by Geometric Series
This Demonstration shows graphically and numerically the quality of approximating the function values of
for any
by the Taylor polynomial
, where
.
Contributed by:
Reinhard Simonovits
With additional contributions by:
Bernd Thaller
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Review questions:
Let
and
. How large is the error?
Let
. For what
is the error less than 0.01?
Let
and
. How large is the error?
Let
. Check the error for
. (The point
is the "best" point since it is the expansion point.)
For
, at which
is the error largest?
For
and
, how large is the error?
For
and
, how large is the error?
RELATED LINKS
Geometric Series
(
Wolfram
MathWorld
)
PERMANENT CITATION
Reinhard Simonovits
"
Quality of Approximation by Geometric Series
"
http://demonstrations.wolfram.com/QualityOfApproximationByGeometricSeries/
Wolfram Demonstrations Project
Published: September 13, 2012
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