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

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๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

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

10.14 Finding Taylor or Maclaurin Series for a Function

#maclaurin

#series

#taylor

โฑ๏ธย ย 1 min read

written by

Peter Cao

peter cao


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Recall the definition of a Taylor series:

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Some Important Maclaurin Series to Remember

There are some Maclaurin series that are so common that they are better to be memorized than derived for the AP test. They are as follows.

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Note that since sine and inverse tangent are odd functions, all the terms have odd powers, which is a contrast to the cosine function, which is even, and thus have even powers. The first four are variations of the geometric series, with the multiplying factor being various powers of x. The series (1 + x)^a is also known as the binomial series with any arbitrary value of a.

IMPORTANT: These formulas only work for Maclaurin series and we cannot substitute (x-a) into these formulas for x to make them a Taylor series!

Problems

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