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Taylor series approximations

8 videos
1 skill
As we've already seen, Maclaurin series are special cases of Taylor series centered at 0. We'll now focus on more generalized Taylor series.

Visualizing Taylor series approximations

VIDEO 6:01 minutes
Using Wolfram Alpha to approximate sin(x)

Generalized Taylor series approximation

VIDEO 7:27 minutes
Approximating a function around a non-zero x value

Visualizing Taylor series for e^x

VIDEO 6:38 minutes
Visualizing Taylor Series for e^x

Finding taylor series

Finding taylor series using the definition

Error or remainder of a Taylor polynomial approximation

VIDEO 11:27 minutes
Understanding the properties of the remainder or error function for an Nth degree Taylor approximation of a function

Proof: Bounding the error or remainder of a taylor polynomial approximation

VIDEO 15:08 minutes
Proof of the Lagrange Error Bound (the bound of the error)