Polynomial Approximation of the Exponential Function

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The graph shows plots of (dashed line) and
for various values of
. It is interesting that for positive values of
, the latter expression is a polynomial that converges from below to
(the blue and violet lines are the polynomials). For negative values of
, the expression is the reciprocal of a polynomial that converges to
from above (the green, yellow, and orange curves are the reciprocals of polynomials).
Contributed by: Hein Hundal (March 2011)
Open content licensed under CC BY-NC-SA
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"Polynomial Approximation of the Exponential Function"
http://demonstrations.wolfram.com/PolynomialApproximationOfTheExponentialFunction/
Wolfram Demonstrations Project
Published: March 7 2011