Consider the following function. f(x) = x In(2x), a = 1, n = 3, 0.7 ≤x≤ 1.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x)= ln(2) + (x-1) (ln(2) +1) + (x-1)² 2! (c) Check your result in part (b) by graphing R,(x). y -0.0002 -0.0004 -0.0006 -0.0008 0.0010 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) * Tn(x) when x lies in R3(x)| ≤ 0.006 0.8 0.9 1.1 1.2 - WebAssign Plot (x-1)³ 3! X 1.3 -0.0002 -0.0004 -0.0006 -0.0008 y 08 0.9

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