Solve the given information Let f(x)=sin⁡x. Use the following values and five-digit rounding arithmetic to...

Lennie Carroll

Lennie Carroll

Answered question


Solve the given information Let f(x)=sinx. Use the following values and five-digit rounding arithmetic to construct the Hermite interpolating polynomial to approximate f(0.34)=sin0.34.

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-01-20Added 109 answers

Consider the provided question, Given, f(x)=sinx We construct a divided- difference table, with each of the interpolation point included twice, that means, x0=x1=0.30,x2=x3=0.32 and x4=x5=0.35. each of the divided differences f[xi,xi+1], where f(x)=sinx and xi=xi+1 is set equal to f(xi).

It follows that Hermit interpolating polynomial is,




Now, evaluating this polynomial at x = 0.34 using five-digit rounding. H5(0.34)=0.29552+0.95534(0.340.30)0.142(0.340.30)2



Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2575 answers

Answer is given below (on video)

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