In calculus, we learn that e = limh0(1 + h)1/h. a. Determine approximations to e corresponding to

Question:

In calculus, we learn that e = limh→0(1 + h)1/h.
a. Determine approximations to e corresponding to h = 0.04, 0.02, and 0.01.
b. Use extrapolation on the approximations, assuming that constants K1, K2 . . . exist with
e = (1 + h)1/h + K1h + K2h2 + K3h3 + · · · , to produce an O(h3) approximation to e, where h = 0.04.
c. Do you think that the assumption in part (b) is correct?