Subject: Numerical Methods

Topic: Roots of Nonlinear Equations

Kindly provide complete solution for each of them. Thank you!

NOTE:

On Quiz 1, kindly use [0,3] as initial approximation.

O7 eLlVIS Activity 1 - ARG Instructions Instructions Use intermediate value theorem to prove that the given equation has a root in the interval (1, 4). Obtain eight (8) iterations of the Bisection method to compute the approximate root of the equation. (x4-4x+4=0 07 eLMS Quiz 1 - ARG Instructions Instructions Find the approximate root of the equation given below using the Secant method correct to three (6) decimal places upto 5 iterations. X 4 - 4x +4 =007 Task Performance 1 ARG Instructions Instructions Upload a photo of your answer sheet showing your name and solution. - Given the equation below, f(:c) = 10 20:22 + 16x2 2.52:3 1. Find the approximate root of the equation using the Secant method correct to six (6) decimal places. Use x0 = 4 and x1 = 5. Seven (7) Iterations 2. Use intermediate value theorem to prove that the equation has a root in the interval (4, 5). Obtain ten (10) iterations of the Bisection method to compute the approximate root of the equation. Limit your computed values to six (6) decimal places