Let f(x) = sin (x) and xo = 0 (a) For n= 1, 2,... show sin...

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Let f(x) = sin (x) and xo = 0 (a) For n= 1, 2,... show sin (x) 2.3 x5 3! 5! x²n-1 (2n-1)! =x- + x²n+1 (2n + 1)! +(-1)". + (−1)n-1 is the Taylor polynomial of degree 2n - 1 and remainder. (b) Using the remainder term, how large should the degree 2n - 1 be chosen to ensure cos (CT) sin (x) - P2n-1(x)| ≤ 10-6 for xe [-1/2, 1/2]? Verify that your answer to (a) is correct by plotting of the error over the interval. Include a copy of the plot with a title and labelled axes. Let f(x) = sin (x) and xo = 0 (a) For n= 1, 2,... show sin (x) 2.3 x5 3! 5! x²n-1 (2n-1)! =x- + x²n+1 (2n + 1)! +(-1)". + (−1)n-1 is the Taylor polynomial of degree 2n - 1 and remainder. (b) Using the remainder term, how large should the degree 2n - 1 be chosen to ensure cos (CT) sin (x) - P2n-1(x)| ≤ 10-6 for xe [-1/2, 1/2]? Verify that your answer to (a) is correct by plotting of the error over the interval. Include a copy of the plot with a title and labelled axes.