The following exercises make use of the functions
169. [Taylor approximations and root finding.) Recall that Newton’s method
a. If f and g are inverse functions, explain why a solution of g(x) = a is the value f(a) of f.
b. Let PN (x) be the Nth degree Maclaurin polynomial of ex. Use Newton’s method to approximate solutions of pN(x) − 2 = 0 for N = 4, 5, 6.
c. Explain why the approximate roots of PN(x) − 2 = 0 are approximate values of In(2).
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