For Problems 1-2, you are to develop Matlab code to solve: f(x) = x - exp( -x ) = 0 For each case, carry out the iterations until the magnitude of the approximate relative error is no more than 10^-10 (10^-8 %). Please submit a hard copy of the code (with explanatory comments embedded within).

1. Use the bisection method with 0 and 1 as the first two guesses.

2. Use the false-position method with 0 and 1 as the first two guesses.

3. Consider the results of Problems 1 and 2. For each method, plot (on the same graph), the approximate relative error (y-axis) versus the number of iterations (x-axis). Use a log scale for the y-axis and a linear scale for the x-axis. Do the approximate relative errors for each method decrease exponentially? Explain.

4. Explain why the false-position method tends to converge more rapidly than does the bisection method.

For Problems 1-2, you are to develop Matlab code to solve: f(x)-x-exp(-x) = 0 For each case, carry out the iterations until the magnitude of the approximate relative error is no more than 10-10 (10-8 %). Please submit a hard copy of the code (with explanatory comments embedded within) Use the bisection method with 0 and 1 as the first two guesses. 1. 2. 3. Use the false-position method with 0 and 1 as the first two guesses. Consider the results of Problems 1 and 2. For each method, plot (on the same graph), the approximate relative error (y-axis) versus the number of iterations (x-axis). Use a log scale for the y-axis and a linear scale for the x-axis. Do the approximate relative errors for each method decrease exponentially? Explain Explain why the false-position method tends to converge more rapidly than does the bisection method. 4