PYQs Based Test - 26 : Numerical Methods (Algebraic Equations)

Newton-Raphton iteration formula for finding $\sqrt[3]{C},$ where C > 0 is

The 2${}^{nd}$ approximation to a root of the equation x² - x - 1 = 0 in the interval (1, 2) by Bisection method will be:

The following table lists an nth order polynomial $f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+\dots +a_{1}x+a_0$ and the forward difference evaluated at equally spaced values of x. The order of the polynomial is

The value of the function f(x) is given at n distinct values of x and its value is to be interpolated at the point x* using all the n points.

The estimate is obtained first by the Lagrange polynomial, denoted by I${}_L$, and then by the

Newton polynomial, denoted by I${}_N$.

Which one of the following statements is correct?

If the equation sin (x) = x² is solved by Newton Raphson’s method with the initial guess of x = 1, then the value of x after 2 iterations would be _______