The Maclaurin series for is

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The Maclaurin series for ln⁡(1+x)\ln(1+x) is x−x22+x33−…x-\dfrac{x^{2}}{2}+\dfrac{x^{3}}{3}-\dots. A student approximates ln⁡(1+0.3)\ln(1+0.3) with the first two non-zero terms 0.3−0.3220.3-\dfrac{0.3^{2}}{2}. Which of the following is the best upper bound on the magnitude of the error of this approximation? (a) 0.00270.0027 (b) 0.0090.009 (c) 0.0450.045 (d) 0.0270.027

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