GATE 2023 PI – Question 48

Engineering Mathematics · Numerical Methods · 2 marks · Numerical answer

Apply Newton–Raphson to $x^5-15=0$, starting at x₀ = 1. Find the first approximation x₁ to two decimals.

Show answer and explanation

Correct answer: 3.75 to 3.85

Explanation

$x_1=x_0-f(x_0)/f^\prime(x_0)=1-(1-15)/(5\times1^4)=1+14/5=\mathbf{3.80}$.

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