Problem 1: Theoretical assignment 1. Use Newtons method to solve x + e x = 0 with an accuracy of 3 decimal places.

Problem 1: Theoretical assignment 1. Use Newton's method to solve x + e* = 0 with an accuracy of 3 decimal places. Please show the specific results at each iterative steps until it converges. (Initial guess Xo = -1). 2. Use Secant method to solve x + em = 0 with an accuracy of 3 decimal places. Please show the specific results at each iterative steps until it converges. (Initial guess Xo = -1, x1 = -1.1). 3. Plot absolute value of residual V.S. iterative steps. Note: 1. This is a theoretical assignment, you need to solve it by hand. You can use computer to evaluate exponent function if necessary, but you do not need to program everything. 2. Rough definition of converged solution: the results with 3 decimal places doesn't change, and both methods can get converged results within 10 steps in this case. 3. The solution of Problem 1 should include: (a) Question 1: write down each iterative step of Newton's method, show the specific evaluation to get Ik. Show Ik and the associated residual at each step. (Points: 20) (b) Question 2: write down each iterative step of Secant method, show the specific evaluation to get Xk. Show Ik and the associated residual at each step. (Points: 20) (c) Question 3: only output one figure including both secant and New- ton's methods. 3 axis: iterative steps; y axis: absolute value of residual at each step (You have got these values from Questions 1 and 2.) (Points: 5)