Numerical Method207710 marksNumerical: Newton Raphson methodNewton's method and Convergence
Derive the formula for Newton Raphson Method. Solve the equation using Newton Raphson method. Assume error precision is 0.01. Discuss drawbacks of the Newton Raphson method. x2 + 4x - 9 = 0
Derive the formula for Newton Raphson Method. Solve the equation using Newton Raphson method. Assume error precision is 0.01. Discuss drawbacks of the Newton Raphson method. $x^2 + 4x - 9 = 0$ [10]
- Equation: $f(x) = x^2 + 4x - 9 = 0$ - Error precision: $E = 0.01$ - Initial guess: not specified in the problem, so I take $x0 = 4$ The exact positive root is $x = -2 + \sqrt{13} = 1.60555...$ --- Expand $f(x)$ by Taylor series about $xn$: $$f(xn + h) = f(xn) + h f'(xn) + \frac{h^2}{2!}f''(xn) ...