The Taylor Series Approximation of order n to the (n-times differentiable) function fx is given by:
fnx = fa +f'ax−a+f"a2!x−a2+ ... +fnan!x−an.
Taylor's Theorem essentially states that fn is the best possible degree n polynomial approximation to f about the point a. Specifically, the difference, fx−fnx can be written in the form:
fx−fnx=hnx⋅x−an, where limx→ahnx=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 = sin(x)cos(x)x^3 sinh(x)cosh(x)
order n =
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