Problem 1E: Decide whether the equations form a cubic spline. S(x)={ x3+x1on[ 0,1 ](x1)3+3(x1)2+3(x1)+1on[ 0,2 ]... Problem 2E: Check the spline conditions for { S1(x)=1+2x+3x2+4x3on[ 0,1 ]S2(x)=10+20(x1)+15(x1)2+4(x1)3on[ 1,2 ]... Problem 3E: Find c in the following cubic splines. Which of the three end conditions—natural, parabolically... Problem 4E: Find k1,k2,k3 in the following cubic spline. Which of the three end conditions—natural,... Problem 5E: How many natural cubic splines on [ 0,2 ] are there for the given data (0,0), (1,1), (2,2) ? Exhibit... Problem 6E: Find the parabolically terminated cubic spline through the data points (0,1), (1,1) , (2,1), (3,1),... Problem 7E: Solve equations 3.26 to find the natural cubic spline through the three points (a) (0,0),(1,1),(2,4)... Problem 8E: Solve equations 3.26 to find the natural cubic spline through the three points (a) (0,1),(2,3),(3,2)... Problem 9E Problem 10E: True or false: Given n=3 data points, the parabolically terminated cubic spline through the points... Problem 11E: (a) How many parabolically terminated cubic splines on [ 0,2 ] are there for the given data (0,2),... Problem 12E: How many not-a-knot cubic splines are there for the given data (1,3),(3,3),(4,2),(5,0) ? Exhibit one... Problem 13E: Find b1 and c3 in the cubic spline S(x)={ 1+b1x59x2+59x3on[ 0,1... Problem 14E Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E Problem 20E: Discuss the existence and uniqueness of a not-a-knot cubic spline when n=2 and n=3. Problem 21E Problem 1CP Problem 2CP: Find and plot the not-a-knot cubic spline that interpolates the data points (a)... Problem 3CP: Find and plot the cubic spline S satisfying S(0)=1, S(1)=3, S(2)=3, S(3)=4, S(4)=2 and with... Problem 4CP Problem 5CP Problem 6CP: Find and plot the cubic spline S satisfying S(0)=1, S(1)=3, S(2)=3, S(3)=4, S(4)=2 and with S(0)=2... Problem 7CP Problem 8CP Problem 9CP: Find the clamped cubic spline that interpolates f(x)=Inx at five evenly spaced points in [ 1,3 ],... Problem 10CP: Find the number of interpolation nodes in Computer Problem 9 required to make the maximum... Problem 11CP: (a) Consider the natural cubic spline through the world population data points in Computer Problem... Problem 12CP Problem 13CP: In a single plot, show the natural, not-a-knot, and parabolically terminated cubic splines through... Problem 14CP Problem 15CP format_list_bulleted