1) [25 pt] Dorfman & Daoutidis 6.13 6.13 In the course of solving a boundary value problem for some function c(x) using centered finite differences, there is a subfunction for computing the residuals that has the following structure: 1 function out = problem6_13 2 n = length(c); 3 dx = 2/(n-1); 4 R(1,1) T c(1) 6 for i= 2:n-1 6 R(1,1)= c(i+1) - 2c(i) + c(i-1) (dx)^2*c(i)^2; 7 end R(n,1)=2*c(n-1) + 2*(dx-1) *c (n) -c(n)^2*dx^2; out = R; Answer the following questions about this problem. (a) If x1 = 0, what is Xn? (b) What is the ordinary differential equation solved by this program? (c) What are the boundary conditions? (d) Write a subfunction that takes the vector c as its input and returns the Jacobian needed for the Newton- Raphson solution of the