In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function

0.75x3 – 2x2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations.

Which of the following is TRUE?    

Newton-Raphson method is used to compute a root of the equation x² - 13 = 0 with 3.5 as the initial value. The approximation after one iteration is

The Newton-Raphson iteration can be used to compute the  

Consider the function f(x) = x² - 2x - 1. Suppose an execution of the Newton- Raphson method to find a zero of f(x) starts with an approximation x₀ = 2 0f x. What is the value of x₂, 'the approximation of x' that the algorithm produces after two iterations, rounded to three decimal places?

 

A piecewise linear function f(x) is plotted using thick solid lines in the figure below If we use the Newton-Raphson method to find the roots of f(x) = 0 using x0, x1 and x2 respectively as initial guesses, the roots obtained would be  

   

The Newton-Raphson method is to be used to find the root of the equation f(x)=0 where x_o is the initial approximation and f' is the derivative of f. The  method converges  

The Newton-Raphson method is used to find the root of the equation x² − 2 = 0. If the iterations are started form –1, the iterations will

   

The iteration formula to find the square root of a positive real number b using the Newton Raphson method is