AP Calc Crash Course for Spring 2021 โ™พ๏ธ

Get unit reviews, practice essays, and live support!

ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

10.11 10.11 Finding Taylor Polynomial Approximations of Functions

#taylor

#approximation

โฑ๏ธย ย 1 min read

written by

Peter Cao

peter cao


https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(565).png?alt=media&token=5dbce567-6f27-4aff-8a3f-914fcbcfbb94

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!

continue learning

Slide 1 of 17
Fiveable Logo

2550 north lake drive
suite 2
milwaukee, wi 53211

92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.

*apยฎ and advanced placementยฎ are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.

ยฉ fiveable 2020 | all rights reserved.