Find the tangent line to the graph of \(f(x)=\sqrt{1-x ... {2}\text{.}\) Use one iteration of Newton's method to find a better approximation to \(x\text{.}\) Simplify your answer as far as possible.

Newton's Method is a technique for approximating a root to an equation of the form \(f(x)=0\). What is required is an initial estimate for the root, called \(x_1\), and an iterative formula ... and ...

Newton method, invented by physicist Isaac Newton about 300 years ago, is an algorithm that still plays an important role in a wide range of fields, including logistics, financial engineering ...