In the Newton-Raphson method, an initial guess of $x_0= 2 $ is made and the sequence $x_0,x_1,x_2\:\dots$ is obtained for the function $0.75x^3-2x^2-2x+4=0$ Consider the statements $x_3\:=\:0$ The method converges to a solution in a finite number of iterations. Which of the following is TRUE? Only I Only II Both I and II Neither I nor II

Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.

The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above