Consider the following function. f(x) = In(1 + 2x), a =4, n = 3, 3.7 5 x S 4.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(X) = IR3(X)IS (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 six decimal places.) (c) Check your result in part (b) by graphing |Rn(x)I. 4 4 -61 38 W X 8. x 10 3.9 4.0 4.1 42 4.3 -2. X 10-6 6. x 10-6 -4. x 10-6 4. x 10-6 -6.x 10-6 2. x 10-6 O-8. X 10-6 O 3.8 3.9 4.0 4.14 4.2 4.3 X y 3.8 3.9 X 8. x 10 61 4.1 -2. x10-6 4.2 4.3 6. x 10-6 -4. X 10-6 4. x 10-6 -6. x 10-6 2. X 10-6 O-8. X 10-6 O 3.8 3.9 4.0 4.1 4.2 . X 4.3