Homework 9Math 371, Fall 2011Assigned:Thursday, November 10, 2011Due:Thursday, November 17, 2011•Clearly label all plots usingtitle,xlabel,ylabel,legend•Use thesubplotcommand to compare multiple plots•Include printouts of all Matlab code, labeled with your name, date, and section.•Add 12 for page numbers in the international edition.(1)(Interpolating Polynomials)The functionf(x) = 1/(x+ 1)is given at the four pointsx0= 1,x1= 2,x2= 3,x3= 4.(a) Write the interpolating polynomial in Lagrange form.(b) Write the interpolating polynomial in Newton form.(c) Evaluatef(1.5)andf(5)using the interpolating polynomial. Which approximate valueis more accurate?(d) Use the error formula to find an upper bound on the maximum error||f-p3||∞= max1≤x≤4|f(x)-p3(x)|.(2)(Choice of Interpolation Points)This question investigates how different interpolationpoints affect the accuracy of the interpolation. Letf(x) =120x2+1.(a) Compute and plot the interpolating polynomial forf(x)using the equally spaced pointsx0=-1,x1= 0,x2= 1.(b) The third Chebyshev polynomial is
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