Solved: To accurately approximate f (x) = ex for inclusion in a mathematical library, we
Chapter 8, Problem 13(choose chapter or problem)
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.
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