To accurately approximate f (x) = ex for inclusion in a mathematical library, we first restrict the domain of f . Given a real number x, divide by ln√10 to obtain the relation
x = M · ln√10 + s,
Where M is an integer and s is a real number satisfying |s| ≤ 1/2 ln√10.
a. Show that ex = es · 10M/2.
b. Construct a rational function approximation for es using n = m = 3. Estimate the error when 0 ≤ |s| ≤ 1/2 ln√10.
c. Design an implementation of ex using the results of part (a) and (b) and the approximations
1/ln√10 = 0.8685889638 and √10 = 3.162277660.