Starting from $$\,{x_0} = 1,\,\,$$ one step of Newton - Raphson method in solving the equation $${x^3} + 3x - 7 = 0$$ gives the next value $${x_1}$$ as

The order of error in the simpson's rule for numerical integration with a step size $$h$$ is

Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}}$$ order Runge-Kutta method with step size $$h=0.1$$ is

Simpson's rule for integration gives exact result when $$f(x)$$ is a polynomial function of degree less than or equal to ________.