GATE 2025 AE – Question 44

Engineering Mathematics · Numerical Methods: Bisection and Newton-Raphson, numerical differentiation, trapezoidal and Simpson's rules · 2 marks · Numerical answer

An approximate solution of the equation $x^3 - 17 = 0$ is to be obtained using the Newton-Raphson method. If the initial guess is $x_o = 2$, the value at the end of the first iteration is $x_1 = $ _____ (rounded off to two decimal places).

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Correct answer: 2.74 to 2.76

Explanation

$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 2 - \frac{8 - 17}{3 \times 4} = 2 + 0.75 = 2.75$.