Find the solution obtained at the end of the first iteration by the Newton-Raphson method for the equation f(x) = x3 - x - 1, taking the initial guess as x0 = 1.

Given the initial value problem dydx = x + y, y(0) = 1. Using the 4th order Runge-Kutta method with step size h = 0.1, calculate the approximate value of y(0.1).

Given the initial value problem dydx = x + y with y(0) = 1 and step size h = 0.1, find the approximate value of y(0.1) using one step of Euler's Method.