ADV018 · Advanced mathematics · Class 12 + B.Tech
Newton-Raphson method
The Newton–Raphson method finds a root by sliding down tangent lines: from a guess xₙ, the tangent crosses the axis at a better guess.
xₙ₊₁ = xₙ − f/f′Newton-Raphson method
📐 Formula
xₙ₊₁ = xₙ − f(xₙ)/f′(xₙ); for √a: xₙ₊₁ = (xₙ + a/xₙ)/2
✏️ Worked example
√2 from x₀ = 1: x₁ = 1.5, x₂ = 1.4167, x₃ = 1.41422 — correct to 5 places in three steps.
🌍 Where it is used
Calculators computing square roots; engineering solvers.
❓ Quick check
Newton's method needs the function's…
🏋️ Practice
EasyOne step for √10 from x₀ = 3?
Answer: 3.1667
MediumWhat if f′(xₙ) = 0?
Answer: The method fails (division by zero)
ChallengeFormula for √a?
Answer: xₙ₊₁ = (xₙ + a/xₙ)/2