Newton-Raphson iteration formula for finding ∛c, where c > 0, is:
1996
Newton-Raphson iteration formula for finding ∛c, where c > 0, is:
- A.
xₙ₊₁ = (2xₙ³ + ∛c) / (3xₙ²)
- B.
xₙ₊₁ = (2xₙ³ - ∛c) / (3xₙ²)
- C.
xₙ₊₁ = (2xₙ³ + c) / (3xₙ²)
- D.
xₙ₊₁ = (2xₙ³ - c) / (3xₙ²)
Show answer & explanation
Correct answer: C
To find ∛c, solve f(x) = x³ - c = 0.
Newton-Raphson uses xₙ₊₁ = xₙ - f(xₙ)/f′(xₙ). Here, f′(x) = 3x².
So, xₙ₊₁ = xₙ - (xₙ³ - c)/(3xₙ²) = (3xₙ³ - xₙ³ + c)/(3xₙ²) = (2xₙ³ + c)/(3xₙ²).
Therefore, the correct option is C.