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Unit 10

10.11 Finding Taylor Polynomial Approximations of Functions

1 min readโ€ขdecember 14, 2020

peter-cao

Peter Cao


AP Calculus AB/BCย โ™พ๏ธ

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In the second, smaller part of the guide, we will be talking about function approximations, which is basically how to find an estimate for the value of function. This is used in many parts of science and engineering and is where the approximation sin(x) ~ x comes from. For the ease of studying, I will be switching some of the topic orders from what College Board has prescribed. To start, letโ€™s talk about power series, and donโ€™t confuse it with a p-series!

What are Taylor Series, and how do you find them?

The Taylor Series is the name for the series approximation of functions, and it can be found by the following formula.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(810).png?alt=media&token=521c3217-683d-48d4-bb81-da07152fe715
Know it or not, you have actually worked with Taylor polynomials before! The tangent line approximation is actually the first-order Taylor polynomial of a function!

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