5.18 Taylor and maclaurin series
Taylor and maclaurin series
Lessons
Notes:
Note * We can represent a function $f(x)$ about $x=a$ as a Taylor Series. A Taylor Series is in the form
$\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(xa)^n$
where $f^{(n)}(a)$ is the $n$'th derivative at $x=a$. If $a=0$, then we call it a Maclaurin Series. A Maclaurin Series is in the form:
$\sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}x^n$
Here are some formulas that may be of use:
$e^x=\sum_{n=0}^{\infty}\frac{x^n}{n!}$
$sin(x)=\sum_{n=0}^{\infty}\frac{(1)^nx^{2n+1}}{(2n+1)!}$
$cos(x)=\sum_{n=0}^{\infty}\frac{(1)^nx^{2n}}{(2n)!}$

1.
Maclaurin Series
Find the Taylor or Maclaurin Series of the following functions without using the formulas: 
2.
Using the Formula to Find the Maclaurin Series
Use the formulas to find the Maclaurin Series for the following functions: