# Euler's Method for the Exponential Function

Euler's Method for the Exponential Function

For each value of , the sequence (x)= converges to . Also, if (t) is the Euler method approximation to the solution of the differential equation , on the interval with , then (t) (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 .

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y(0)=1

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h=x/n

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