Question: Consider the following function. f(x) = x /3, a=1, n=3, 0.75x$ 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number

Consider the following function. f(x) = x /3, a=1, n=3, 0.75x$ 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) & T (x) when x lies in the given interval. (Round your answer to eight decimal places.) IR,(x )Is (c) Check your result in part (b) by graphing |R (x)|. 0.0005 0.0005 X 0.0004 08 0.9 1.0 _ 1.1 1.2 1.3 0.0004 0.8 0.9 1.0 1.1 1.2 1. -0.0001 -0.0001 0.0003 0.0003 - 0.0002 -0.0002 0.0002 0.0002 -0.0003 - 0.0003 0.0001 0.0001 -0.0004 -0.0004 X 0.8 0.9 1.0 1.1 1.2 1.3 -0.0005 0.8 0.9 1.0 1.1 1.2 1.3 -0.0005 O

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