In this assignment, we will t a parametric curve using cubic splines, solve for intersections, and integrate numerically to nd the length of a curve segment. You may use the MATLAB functions on the course web page, in particular ncspline.m, splineeval.m, and diffsplineeval.m. 1. Consider a parameteric curve (x(t),y(t)), 0 t 5 (see gure below). The position of the curve is given at 6 parameter values: t x(t) y(t) 0 1.0 1.0 1 1.5 0.5 2 2.0 1.0 3 2.0 1.5 4 2.5 1.5 5 2.5 1.0 Approximate the curve by tting natural cubic splines to this data, independently for x(t) and y(t). Plot the curve in MATLAB by plot(xx,yy, x,y,'o'), axis equal, grid on where x,y contain the given values and xx,yy contain the spline data evaluated for a large number of parameter values between 0 and 5. Your report should contain your MATLAB commands, the computed aj , bj , cj , dj values for x(t),y(t), and a plot of the curve. 2. Use Newton's method to nd the parameter values t1 and t2 where the curve intersects the line y = 1.2. Use the provided MATLAB functions splineeval.m and diffsplineeval.m. Give a short justication for