πŸ“š

Β >Β 

♾️ 

Β >Β 

β™Ύ

10.11 Finding Taylor Polynomial Approximations of Functions

1 min readβ€’december 14, 2020

Athena_Codes

Athena_Codes


AP Calculus AB/BC ♾️

279Β resources
See Units

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, let’s talk about power series, and don’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!
Browse Study Guides By Unit
πŸ‘‘Unit 1 – Limits & Continuity
πŸ€“Unit 2 – Fundamentals of Differentiation
πŸ€™πŸ½Unit 3 – Composite, Implicit, & Inverse Functions
πŸ‘€Unit 4 – Contextual Applications of Differentiation
✨Unit 5 – Analytical Applications of Differentiation
πŸ”₯Unit 6 – Integration & Accumulation of Change
πŸ’ŽUnit 7 – Differential Equations
🐢Unit 8 – Applications of Integration
πŸ¦–Unit 9 – Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)
β™ΎUnit 10 – Infinite Sequences & Series (BC Only)
πŸ“šStudy Tools
πŸ€”Exam Skills

Fiveable
Fiveable
Home
Stay Connected

Β© 2024 Fiveable Inc. All rights reserved.


Β© 2024 Fiveable Inc. All rights reserved.