Note: The Khan academy videos call the Taylor’s Inequality Theorem “Lagrange error bound” or “Taylor’s Remainder Theorem”.
Lecture videos:
Taylor polynomial remainder (part 1): https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/error-or-remainder-of-a-taylor-polynomial-approximation
Taylor polynomial remainder (part 2): https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/proof-bounding-the-error-or-remainder-of-a-taylor-polynomial-approximation
Visualizing Taylor polynomial approximations: https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/visualizing-taylor-series-for-e-x
If you are short on time, you can go straight to the example videos and online practices:
Worked example: estimating sin(0.4) using Lagrange error bound: https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/lagrange-error-bound-for-sine-function
Worked example: estimating e(x) using Lagrange error bound: https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/lagrange-error-bound-exponential-example
Practice: Lagrange error bound: https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/e/taylor-polynomial-approximation
Worked example: Taylor polynomial of derivative function: https://www.khanacademy.org/math/calculus-home/series-calc/taylor-series-calc/v/evaluating-taylor-polynomial-of-derivative
All the other videos in this tutorial, called Taylor & Maclaurin polynomials intro , are done the same way as in our textbook, so watching any of the videos and doing any of the online practices in this tutorial should be helpful.