Assignment:
The Newton-Raphson Method
Q1. Consider the function f(x) = x2- 2 .
i) Show, graphically or otherwise, that the equation f(x) = 0 has a root α in the interval (1,2). Show that α =√2 .
ii) Use the secant method, with the function f(x) and starting values, 1 and 2, to find an estimate of √2 correct to three decimal places.
Q2. Verify that x3 +x -1 = 0 has just one real zero and that it lies between 0 and 1 and give solution to five decimal places using the Newton-Raphson method.
Q3. Locate all the zeros of 2x3 - 6x .
Provide complete and step by step solution for the question and show calculations and use formulas.