EXAMPLE 8 Working with the remainder In Example 4b of Section 11.2, we show that the nth-order Taylor polynomial for f(x) = In (1 – x) centered at 0 is п k P„(x) = -E x? x 3 п k=1 a. Find a bound on the error in approximating In (1 – x) by p;(x) for values of x in the interval [-.]. b. How many terms of the Taylor polynomial are needed to approximate values of f(x) = In (1 – x) with an error less than 10-³ on the interval [-}, 4]?

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