Question

Find two roots of the equation f(x)=2x³−7x+2. Use Fixed point Iteration. 2. Find the root of the equation x=cosx, using simple iteration method. Where is the accuracy =1∗10⁻²

Answer 1

To find the roots of the given equations, we can use the Fixed Point Iteration and Simple Iteration methods.

Step-by-step explanation:

To find two roots of the equation f(x) = 2x³ - 7x + 2 using the Fixed Point Iteration method, we first need to rewrite the equation in the form x = g(x).

Rearranging the equation, we get x = (2x³ + 2) / 7.

Starting with an initial guess, we substitute it into the equation and repeat the process until we get two converging values for x.

Similarly, to find the root of the equation x = cos(x) using the Simple Iteration method with an accuracy of 1×10⁻², we rearrange the equation to get x = arccos(x), which is our g(x) function.

Then, we start with an initial guess, substitute it into the equation, and repeat the process until we achieve the desired accuracy.