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Using Taylor Polynomials- Some Examples

In this video, Professor Kate demonstrates how to use Taylor polynomials to estimate the values of different types of functions — including logarithmic, trigonometric, exponential, and rational examples. You’ll see how the same underlying idea applies across very different functions: using derivatives at a single point to build local polynomial approximations. This lesson focuses on interpreting and applying Taylor polynomials to real examples, setting the stage for later videos on accuracy and error estimation. ✨ Topics Covered: Approximating functions with Taylor polynomials Comparing polynomial estimates to actual function values 00:00 Introduction 00:12 Taylor Polynomial Formula 00:42 Example 1: Logarithmic approximation 04:12 Example 2: A Trigonometric Approximation 06:58 Example 3: An Exponential Approximation 10:18 Example 4: A Rational Approximation 14:35 Wrap Up