For x > 0 consider the equation x + ln x = 0. It is a reformulation of the equation of Example 3.4. (a) Show analytically that there is exactly one root, 0 < x < . (b) Plot a graph of the function on the interval [0.1, 1]. (c) As you can see from the graph, the root is between 0.5 and 0.6. Write MATLAB routines for finding the root, using the following: i. Thebisectionmethod,withtheinitialinterval[0.5,0.6].Explainwhythischoiceof the initial interval is valid. ii. A linearly convergent fixed point iteration, with x0 = 0.5. Show that the conditions of the Fixed Point Theorem (for the function g you have selected) are satisfied. iii. Newtons method, with x0 = 0.5. iv. The secant method, with x0 = 0.5 and x1 = 0.6. For each of the methods: Use |xk xk1| < 1010 as a convergence criterion. Print out the iterates and show the progress in the number of correct decimal digits throughout the iteration. Explain the convergence behavior and how it matches theoretical expectations.