f(x) = x sin(x), a = 0, n = 4, -0.6 x 0.6 (a) Approximate f...

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f(x) = x sin(x), a = 0, n = 4, -0.6 x 0.6 (a) Approximate f by a Taylor polynomial with degreen at the number a. T4(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 M up to the nearest integer. Round your a to four decimal places.) |R(x)| (c) Check your result in part (b) by graphing IR, (X). y -0.6 0.4 -0.2 O-0.6 -0.4 -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 -0.0006 y 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 -0.2 0.2 0.4 0.2 0.4 X 0.6 + X 0.6 -0.6 -0.4 -0.2 O-0.6 -0.4 y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 - 0/0006 -0.2 y 00006 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.2 0.4 0.4 0.6 0.6 X X f(x) = x sin(x), a = 0, n = 4, -0.6 x 0.6 (a) Approximate f by a Taylor polynomial with degreen at the number a. T4(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 M up to the nearest integer. Round your a to four decimal places.) |R(x)| (c) Check your result in part (b) by graphing IR, (X). y -0.6 0.4 -0.2 O-0.6 -0.4 -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 -0.0006 y 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 -0.2 0.2 0.4 0.2 0.4 X 0.6 + X 0.6 -0.6 -0.4 -0.2 O-0.6 -0.4 y -0.0001 -0.0002 -0.0003 -0.0004 -0.0005 - 0/0006 -0.2 y 00006 0.0005 0.0004 0.0003 0.0002 0.0001 0.2 0.2 0.4 0.4 0.6 0.6 X X