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Error Estimates in Taylor Polynomials

In this video, Professor Kate explains how Taylor’s Inequality provides an upper bound on the error when we approximate a function with a Taylor polynomial. You’ll learn how to use the remainder term |R_n(x)| ≤ M|x - a|^(n+1) / (n+1)! to estimate how accurate your approximation is — even when you can’t compute the exact remainder! We’ll discuss what the inequality mean and how to find a suitable M. Perfect for Calculus II students learning how to trust their Taylor polynomials! 00:00 Introduction 00:16 What is a Taylor Polynomial? 00:40 Understanding the Error in a Taylor Polynomial Estimate 02:46 Estimating the Error 03:36 Example 1: Estimating error in sin(pi/16} 07:52 Wrap Up