Khan Academy: Calculus: Bounding the Error of a Taylor Polynomial Approximation

Video shows how to calculate the Lagrange error bound for a Taylor series polynomial approximation. [11:52]

Video first reviews the formula for a Taylor series expansion and then defines the error function to be the difference between the polynomial approximation and the actual function. Properties of the derivatives of the error function are...

Video lesson finishing the derivation of the formula for the Maclaurin series and then applying it to find the polynomial approximation for e^x. [10:09]

Video lesson showing the formula for a Taylor series expansion to five terms and uses it to approximate the cosine function. Includes the graphs of a specific number of terms of the approximate function using a graphing calculator. [18:05]

Video lesson using a Maclaurin series to approximate an exponential function by using a polynomial function and relates its polynomial approximation to that for the sine and cosine functions. [6:10]

Video continues a discussion about the relationship between the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series and uses those to derive Euler's formula and Euler's identity. [10:18]

Video lesson using a Maclaurin series to approximate a cosine function by using a polynomial function. Generalizes the expansion of cosine using sigma notation. [9:59]

Video lesson relating the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series. [9:59]

Video lesson showing how to approximate a function at 0 using a polynomial by deriving the first three terms for the formula of a Maclaurin series. [9:45]

Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. Generalizes the expansion of sine using sigma notation and relates it to the expansion for cosine. [9:24]