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

Lennie Carroll

Lennie Carroll

Answered question

2021-01-19

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.
xf(x)f(x)0.300.295520.955340.320.314570.949240.350.342900.93937

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).
xif[xi]f[xi,xi+1]0.300.295520.955340.142001.050020.732431.410.300.295520.952500.163000.01340.838660.320.314570.949240.163670.055330.320.314570.944330.165330.350.342900.939370.350.34290

It follows that Hermit interpolating polynomial is,

H5(x)=0.29552+0.95532(x0.30)0.142(x0.30)2

1.05(x0.30)2(x0.32)+20.732(x0.30)2(x0.32)2

431.41(x0.30)2(x0.32)2(x0.35)

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

1.05(0.340.30)2(0.340.32)+20.732(0.340.30)2(0.340.32)2

431.41(0.340.30)2(0.340.32)2(0.340.35)H5(0.34)=0.33349

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-16Added 2605 answers

Answer is given below (on video)

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