Homework 4.docx - Michelle Gonzalez Homework 4 1 Consider...

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Michelle Gonzalez Homework # 4 11/03/20151.Consider the three data points (1, 0), (2, ln 2), and (4, ln 4).a.Use Newton’s divided differences to find the interpolating polynomial that passes through allthree points.
4)(2(62ln)1(2ln)(xPc.Develop an error bound for your approximation in part b. Is this a bound on the absolute error orthe relative error?
)b.Use the result from part (a) to obtain an approximation of ln 3.
PxPc.Develop an error bound for your approximation in part b. Is this a bound on the absolute error orthe relative error?
d.Compare the actual error of your approximation of ln 3 using a “true” value obtained with the lnfunction (log in Matlab) to your error bound. Indicate whether you find the error bound close toor far from the true error and explain why that is the case.
2.The horse Secretariat won the Kentucky Derby in 1973 by running the 1.25-mile distance in under2 minutes (1 minute, 59.4 seconds). A remarkable feature of this winning run was that Secretariatran each 0.25-mile segment of the course faster than the previous segment. The table below givesthe time at which Secretariat reached each listed distance.a.Find the cubic polynomial that interpolates the data set at the four distances ??
b.Find the quintic polynomial that interpolates the data set at all six distances (include a plot ofinterpolated distance vs. time in your writeup) and use it to estimate Secretariat’s speed inmiles per hour at the beginning and end of the race.
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