Taylor's Theorem - Maple Help

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Taylor's Theorem

Main Concept

The Taylor Series Approximation of order n to the (n-times differentiable) function fx is given by:

 

fnx = fa +f'axa+f"a2!xa2+ ...  +fnan!xan. 

 

Taylor's Theorem essentially states that fn is the best possible degree n polynomial approximation to f about the point a. Specifically, the difference, fxfnx can be written in the form:

 

fxfnx=hnxxan, where limxahnx=0.

 

The special case of Taylor Series in which a = 0 is known as the Maclaurin Series.

 

Pick the function you want to approximate and adjust the sliders to modify the settings.

fx = 

a  = 

order n  = 

fnx = 

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