Let Pn(x) be the nth Taylor polynomial for f (x) = ex expanded about x0 = 0.

Question:

Let Pn(x) be the nth Taylor polynomial for f (x) = ex expanded about x0 = 0.
a. For fixed x, show that pn = Pn(x) satisfies the hypotheses of Theorem 2.14.
b. Let x = 1, and use Aitken's (2 method to generate the sequence 0, . . . , 8.
c. Does Aitken's method accelerate convergence in this situation?