I made this list of Khan Academy videos for two students who are out of town this week, but you can watch these as well if you want better understanding of Taylor polynomials, especially how to apply the Taylor’s Inequality theorem for finding error bounds. Past Calc 2 students have said that this topic was one of the most challenging for them.
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.