Question

Raphson method is applicable to the solution of which equation?

Answer 1

Newton Raphson method of solution $f$ numerical equation is not preferred when the graph of $f(x)$ is nearly horizontal when it crosses the X-axis. And it is used for finding the roots for nonlinear equations. Formula which is used to make the solution for equation that is ${{x}_{1}}={{x}_{0}}-\dfrac{f({{x}_{0}})}{{{f}^{'}}({{x}_{0}})}$ this formula is used to solve the problems.

Complete answer:
First of all we need to know about Newton Raphson method. So, Newton Raphson method is a numerical solution which provides better approximation to the roots of a real-valued function.
The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative ${{f}^{'}}$, and an initial guess ${{x}_{0}}$ for a root of $f$. If the function satisfies sufficient assumptions and the initial guess is close, then
${{x}_{1}}={{x}_{0}}-\dfrac{f({{x}_{0}})}{{{f}^{'}}({{x}_{0}})}$
$f({{x}_{0}})=$ Function at ${{x}_{0}}$
${{f}^{'}}({{x}_{0}})=$ First derivative of the function at ${{x}_{0}}$
${{x}_{0}}=$ Initial value
This process may be repeated as many times as necessary to get the desired accuracy. In general, for any $x$-value ${{x}_{n}}$ next value is given by
${{x}_{n+1}}={{x}_{n}}-\dfrac{f({{x}_{n}})}{{{f}^{'}}({{x}_{n}})}$
​Numerical solution or approximate solution or Newton Raphson method is applicable for the solution to the transcendental equation.
Transcendental equation is an equation containing a transcendental function of the variable (s) being solved for. Such equations often do not have closed-form solutions.
Approximate numerical solutions to transcendental equations can be found using numerical, analytical approximations, or graphical methods or Newton Raphson method.
So, the correct answer is Newton Raphson method is applicable to the solution of a transcendent equation.

Note:
Always remember that in numerical solution or Newton Raphson method for roots or function is differentiable. Even a graphical method is useful for solving the transcendental equation. So, in this type of transcendental equation or value of roots we can solve it by using Newton Raphson method.