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Engineering Mathematics
Numerical Methods
GATE 2010
Medium

Newton-Raphson method is used to compute a root of the equation x² − 13 = 0 with 3.5 as the initial value. The approximation after one iteration is:

  • A3.575
  • B3.677
  • C3.667
  • 3.607

Explanation

x₁ = x₀ − f(x₀)/f'(x₀) = 3.5 − (3.5² − 13)/(2×3.5) = 3.5 − (12.25 − 13)/7 = 3.5 − (−0.75/7) = 3.5 + 0.10714 ≈ 3.607.

Source: GATE CS 2010 (2010)

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