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  3. AP Calculus AB/BC
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Representing Functions as Power Series

Abigail Young

Abigail Young

5 min read

Study Guide Overview

This study guide covers representing functions as power series, an AP Calculus BC topic. It introduces power series and provides key examples using exe^xex, sin(x)sin(x)sin(x), and cos(x)cos(x)cos(x). It also demonstrates finding power series representations for functions and their derivatives. Finally, it includes a practice FRQ from the 2022 AP Calculus BC exam related to power series.

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Previous Topic - Finding Taylor or Maclaurin Series for a Function

Question 1 of 7

Which of the following expressions represents a power series? 🤔

1 + x + x^2 + x^3 + ...

1 + x + x^2 + x^3 + ... + x^n

1 + x^{-1} + x^{-2} + x^{-3} + ...

1 + x + \sqrt{x} + x^{3/2} + ...