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GATE 2016 ME (ME3) – Question 15

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 1 mark · Multiple choice

For $f(x)=x^3+x-1$, one Newton–Raphson iteration from $x_0=1$ gives ______.

  1. 0.682
  2. 0.686
  3. 0.750
  4. 1.000

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Correct answer: (C) 0.750

Explanation

Newton’s formula is x₁=x₀−f(x₀)/f′(x₀). At x₀=1, f=1 and f′=3x₀²+1=4, so x₁=1−1/4=**0.75, C**. This is the first approximation rather than the converged root.