Newton's Method in Calculus | Formula, Equation & Examples

SOLVED:A variant of Newton-Raphson for roots of higher multiplicity. Each polynomial in Exercises 33-36 has one root c of multiplicity m=2. Approximate each such root using the initial estimate x1=c 1 / 2 and the formula xj 1=xj-m (p(xj))/(p^'(xj)) . In each case, terminate the process at the smallest value of M for which |xM-c|<5 ×10^-4. What is M ? Compare the number M with the corresponding number N that results when the unmodified Newton-Raphson Method is used.

mathswithmuza on Instagram: "Newton–Raphson is an iterative method for finding solutions to equations of the form f(x) = 0. Instead of trying to solve the equation directly, it starts with an initial guess and improves that guess step by step. The key idea is to use the tangent line at the current point as a local approximation of the curve. If you know the value of the function and its derivative at a point, you can follow the tangent line down to where it crosses the x-axis. That crossing beco