a. Show that the polynomial nesting technique described in Example 6 can also be applied to the evaluation of
f (x) = 1.01e4x − 4.62e3x − 3.11e2x + 12.2ex − 1.99.
b. Use three-digit rounding arithmetic, the assumption that e1.53 = 4.62, and the fact that enx = (ex)n to evaluate f (1.53) as given in part (a).
c. Redo the calculation in part (b) by first nesting the calculations.
d. Compare the approximations in parts (b) and (c) to the true three-digit result f (1.53) = −7.61.