Join Our Discord

Learn Moreย ย ๐Ÿ‘‡

caret down
caret up
discord-logo

Join our Discord

1,000s of Fiveable Community students are already finding study help, meeting new friends, and sharing tons of opportunities among other students around the world! Don't miss out!ย  ๐ŸŽ‰

group of students
group of students

โ™พ๏ธย ap calc

ย ย >ย ย 

โ™พย Unit 10

ย ย โ€ขย ย โฑ๏ธ1 min read

10.11 Finding Taylor Polynomial Approximations of Functions

Peter Cao

peter cao

โฑ๏ธ December 14, 2020

๐Ÿ“…โŒจ๏ธ

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!

A tent in the woods with a fire

Get your ap calc survival pack!

Download our ap calc survival pack and get access to every resource you need to get a 5.

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)

continue learning

Slide 1 of 17
Fiveable

Join Our Discord

discord-logo

Fiveable Community students are already meeting new friends, starting study groups, and sharing tons of opportunities for other high schoolers. Soon the Fiveable Community will be on a totally new platform where you can share, save, and organize your learning links and lead study groups among other students!๐ŸŽ‰

*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 2021 | all rights reserved.

2550 north lake drive
suite 2
milwaukee, wi 53211