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For each value of

, the sequence

converges to

. Also, if

is the Euler method approximation to the solution of the differential equation

on the interval

with

, then

(the red curve) converges to

for each

in the interval. The points generated by Euler's method are marked in green. Observe that for any

, the error between the approximation and the real value increases with the value of

Contributed by: Arnaud Crouzet

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Euler's Method for the Exponential Function