Tuesday, June 04, 2013
Taylor series worth memorizing
About x=0:
| 11−x=1+x+x2+⋯ex=1+x+x22!+x33!+⋯ln(1+x)=x−x22+x33+⋯cosx=1−x22!+x44!+⋯sinx=x−x33!+x55!+⋯arctanx=x−x33+x55+⋯ |
About x=a:
| f(x)=f(a)+f′(a)(x−a)+f″ |
Let h = x - a:
| \begin{aligned} f(a + h) = f(a) + f'(a) h + f''(a) \frac{h^2}{2!} + f'''(a) \frac{h^3}{3!} + \cdots \end{aligned} |
