Power Series: Ace AP Calculus BC Like a Pro

Representing Functions as Power Series

Abigail Young

5 min read

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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 $e^x$ , $sin(x)$ , and $cos(x)$ . 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.

#10.15 Representing Functions as Power Series

Congrats congrats! You made it to the last AP Calculus BC topic! In this key topic, you’ll be deriving power series using different techniques you’ve learned throughout this course.

#🟦Power Series

A power series, similar to what you’ve learned about Taylor polynomials, are a representation of a function using an infinite series of polynomials. It is generally expressed by the following below, where n is a non-negative integer, $a_n$ is a sequence of real numbers, and r is a real number.

$\displaystyle\sum_{n=0}^{∞}{a_n(x-r)}$

For the AP Calculus BC exam, memorizing these three frequently...

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