Topics
Maclaurin Series Basics
0 of 0 exercises completed
Learn to approximate complicated functions with polynomials and higher order derivatives.
Want a deeper conceptual understanding? Try our interactive lesson!
General formula
AHL 5.19
Maclaurin series allow us to approximate arbitrary functions as polynomials.
The Maclaurin series for a function f is given by
f(x)=f(0)+xf′(0)+2!x2f′′(0)+⋯📖
In summation form:
f(x)=n=0∑∞n!f(n)(0)xn🚫
e^x
AHL 5.19
The Maclaurin series for ex is
ex=1+x+2!x2+⋯📖
sin(x)
AHL 5.19
The Maclaurin series for sinx is
sinx=x−3!x3+5!x5−⋯📖
cos(x)
AHL 5.19
The Maclaurin series for cosx is
cosx=1−2!x2+4!x4−⋯📖
ln(x+1)
AHL 5.19
The Maclaurin series for ln(x+1) is
ln(x+1)=x−2x2+3x3−⋯📖
arctan(x)
AHL 5.19
The Maclaurin series for arctanx is
arctanx=x−3x3+5x5−⋯📖
Binomial extension for rational exponents
AHL AA 1.10
The binomial theorem can be extended to expansions with rational exponents (n∈Q):
(a+b)n=an(1+n(ab)+2!n(n−1)(ab)2+⋯)📖
Nice work completing Maclaurin Series Basics, here's a quick recap of what we covered:
Skills covered
Exercises checked off
I'm Plex, here to help you understand this concept!