University⏱ 4 min

Newton's Method

Numerical root finding

○Not Started
x0=2.500x1=1.650x2=1.431x3=1.414root≈1.4142
x₀=2.50
Iterations: 4
xn+1=xn−\ racf(xn)f′(xn)x_{n+1} = x_n - \ rac{f(x_n)}{f'(x_n)}

Last x: 1.414214

Newton's method: draw the tangent at a point, find where it crosses the x-axis, repeat there. It converges quadratically – correct digits roughly double each iteration.