5 minute Calculus - FRQ for AP - Taylor Series, Taylor polynomial, and Error in 5 minutes

Free response question on Taylor
1) Write the third-degree Taylor polynomial for f about x = 4
2) What is the radius of convergence of the Taylor series?
3) What is the interval of convergence of the Taylor series?
4) Show that the fifth---degree Taylor polynomial approximates f (5) with error less than 0.0002 (use "Alternating Series Estimation Theorem" and "Lagrange Remainder and Taylor's Inequality")
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Notes: for 3:30 and 4:22, for the last expressions on the last lines, it might be clearer and more correct to say "n+1=6." Either way, when what you have has a derivative with "n", if you want the error, then you work with the next derivative "n+1".
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Questions are my own and are based upon the most common questions for that topic in the AP* exam. The questions are NOT official, but they relate to topics in the official test. (*AP is a trademark [registered / owned] by the College Board, which is not affiliated with, and does not endorse, these videos)