Taylor series and Maclaurin series

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Examples
Lessons
  1. Maclaurin Series
    Find the Taylor or Maclaurin Series of the following functions without using the formulas:
    1. e2xe^{2x} at x=0x=0
    2. x2+3x+1 x^2+3x+1 at x=3x=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) sin (4x)
    2. ex2 e^{x^2}
    3. cos(3x4) cos(3x^4)
  3. Finding the Taylor Series for Sine and Cosine
    Show that sin(x)=sin(x)= n=0(1)nx2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^nx^{2n+1}}{(2n+1)!}
    1. Finding the Taylor Series for Sine and Cosine
      Show that cos(x)=cos(x)= n=0(1)nx2n(2n)!\sum_{n=0}^{\infty} \frac{(-1)^nx^{2n}}{(2n)!}