Problem

(Maclaurin Series Function Approximations) By using the truncated Maclaurin series, a fu...

(Maclaurin Series Function Approximations) By using the truncated Maclaurin series, a function f (x) with n continuous derivatives can be approximated by an nth-degree polynomial

where ci = f ⁽ⁱ⁾(0)/i !.

a. Produce and compare computer plots for f (x) = e^x and the polynomials p₂(x), p₃(x), p₄(x), p₅(x). Do the higher-order polynomials approximate the exponential function e^x satisfactorily on increasing intervals about zero?

b. Repeat for g(x) = ln(1 + x).

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Solutions For Problems in Chapter 1.2

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