Problem
1. Approximate the function lgx with a cubic spline with knots at 2N for N between 1 and 10. Experiment with different placements of knots in the same range to try to obtain a better fit.
2. What will happen in least-squares data fitting if one of the functions fi(x) = 0was the function for some i?
3. Use a least-squares curvefitter to find the values of a and b that give the best formula of the form aN In N +bN for describing the total number of instructions executed when Quicksort is run on a random file.