Chapter 10.3, Problem 12E

Fill in the coefficients of the degree 3 Taylor polynomial for f(x) = sin x centered at x = 3 T3(x) = [ Select ] %D [ Select ] - (x – ) + [ Select ] (x - 5)² 3 [ Select ] - (x - 5)* IT 3

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below: Construct polynomial interpolation in mentioned interval of the functions (a) sinx in [0, 2π] (b) tan (1+x) in [0, 1] (c) exp (2²1) in [2,3] (-) in (-1,1] (d) exp (e) √ in [4,9] Choose the polynomial degree in Problem 1 in such a way that the interpolation error is less than 10-³.

Use the third Taylor polynomial P3(x) for f(x) = x + xlnx about x0 = 1 and evaluate f(2).