There are 8 questions and I need to follow the process in the problem(to fill all the blank that required) 1. (10 points) Use the bisection method with tol = 10−12 to find ALL ZEROS in the interval...

1. (10 points) Use the bisection method with tol = 10−12 to find ALL ZEROS in the interval [0, 1] for the following function: f(x) = x 3 − (a1 − exp(a2x))x 2 + a3x − a4 with a1 = 1.42, a2 = −7.89, a3 = 0.52, a4 = 0.047. Present numerical results in a table as follows: Here, [a, b] is the starting interval used in the bisection method to compute the zero. Put each zero found and the related computational data in one row. Use more rows if more than one zero are found. 2. (10 points) Consider the following nonlinear function: f(x) = sin a1+ (a2− exp(a3x))x 2+ a4x 3  . (a) Use the secant method to compute the zeros of f in the interval [0, 1] with the following parameters: a_1 = 0.1; a_2 = -3.2; a_3 = -5; a_4 = -1; Use the following inputs for the secant method: tol = 10^(-12); nmax = 1000; Present numerical results in a table as follows: 1 zero found a b Iterations Used zero found Residual NOI Add more rows for multiple zeros found. Present your script for generating these numerical results. “NOI” in the table means the number of iteration actually used by the method. (b) Use Newton’s method to compute the zeros of f in the interval [0, 1] with the following parameters: a1 = 0.2; a2 = 4.5; a3 = -5; a4 = -1; Use the following inputs for the Newton’s method: tol = 10^(-12); nmax = 1000; Present numerical results in a table as follows: zero found Residual NOI Add more rows for multiple zeros found. Present your script for generating these numerical results. “NOI” in the table means the number of iteration actually used by the method 3. (30 points) Consider the following nonlinear system for p, Q1, Q2 and