Section 8.8: Taylor Series (So cool it needs its own theme music)
Recall This is valid on the interval of convergence of the original series.
So what is ?? It must be ex!!
Theorem If f(x) can be written as a power series it must be This is the Taylor series for f. When c = 0,it is called the Maclaurin series for f.
Why? Suppose What is f(c) ??
Converges by ratio test What does it converge to? e2
Mystery Solved: Why does L’Hopital’s Rule work? Why is ?
Euler’s Formula Corollary: