Mathematics

Mathematics

Problem

Consider g(x)=1+xg(x)=\sqrt{1+x} on the domain x>−1x>-1. Let Q2(x)=1+x2−x28Q_2(x)=1+\dfrac{x}{2}-\dfrac{x^2}{8} be its 2nd–degree Maclaurin polynomial. Determine the largest interval [0,r][0,r] (r>0)(r>0) on which the error of using Q2(x)Q_2(x) to approximate g(x)g(x) is less than 0.00010.0001. a) 0≤x≤0.080\le x\le 0.08 b) 0≤x≤0.180\le x\le 0.18 c) 0≤x≤0.100\le x\le 0.10 d) 0≤x≤0.130\le x\le 0.13

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