Taylor and maclaurin series

Lessons

1. Maclaurin Series
   Find the Taylor or Maclaurin Series of the following functions without using the formulas:
   
   1. $e^{2x}$ at $x=0$
   2. $x^2+3x+1$ at $x=3$
2. Using the Formula to Find the Maclaurin Series
   Use the formulas to find the Maclaurin Series for the following functions:
   
   1. $sin (4x)$
   2. $e^{x^2}$
   3. $cos(3x^4)$
3. Finding the Taylor Series for Sine and Cosine
   Show that $sin(x)=$ $\sum_{n=0}^{\infty} \frac{(-1)^nx^{2n+1}}{(2n+1)!}$
4. Finding the Taylor Series for Sine and Cosine
   Show that $cos(x)=$ $\sum_{n=0}^{\infty} \frac{(-1)^nx^{2n}}{(2n)!}$