Newton and Raphson used ideas of the Calculus to generalize this ancient method to find the zeros of an arbitrary equation.
They are in the state of rest or in a state of motion in a straight line
Ideally, quadratic. Please see the link.
An improved root finding scheme is to combine the bisection and Newton-Raphson methods. The bisection method guarantees a root (or singularity) and is used to limit the changes in position estimated by the Newton-Raphson method when the linear assumption is poor. However, Newton-Raphson steps are taken in the nearly linear regime to speed convergence. In other words, if we know that we have a root bracketed between our two bounding points, we first consider the Newton-Raphson step. If that would predict a next point that is outside of our bracketed range, then we do a bisection step instead by choosing the midpoint of the range to be the next point. We then evaluate the function at the next point and, depending on the sign of that evaluation, replace one of the bounding points with the new point. This keeps the root bracketed, while allowing us to benefit from the speed of Newton-Raphson.
Where newton law fail and how?
Square roots are computed using the Babylonian method, calculators, Newton's method, or the Rough estimation method. * * * * * Or the Newton-Raphson method.
You can either use a calculator or a numerical method such as Newton-Raphson (for which you will require a calculator!)
You can find this charge by looking online. Many sites can help you to get the chart you need or explain how to make one.
Joseph Raphson was born in 1648.
Joseph Raphson died in 1715.
Inverse square law of gravity, calculus (which he called fluxions), Newton-Raphson method, decomposition of light from a prism, etc etc. He also made the reflecting telescope.
The Newton - Raphson method of successive approximations is easily implemented on a computer. You make a guess, test it by squaring it and compare it with the original target. JCF