Consider the following function. f(x) = sin(x), a = ₁ n = 4, 0≤x≤ (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) x T (x) when x lies in the given interval. (Round your answer to six decimal places.) IR₂(X)IS (c) Check your result in part (b) by graphing IR,(x). y 0.0005 0.0004 0.0003 0.0002 0.0001 O 0.2 0.4 0.6 0.8 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 94 0.6 0.8 T 1.0 X y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 0.2 0.4 0.6 0.8 1.0 X 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.4 0.6 0.8 1.0 y

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