GATE 2024 CH – Question 50

Engineering Mathematics · Numerical Methods: Algebraic equations, integration, ODEs and finite-difference methods · 2 marks · Numerical answer

The Newton-Raphson method is used to solve $f(x) = 0$, where $f(x) = e^x - 5x$. If the initial guess $x^{(0)} = 1.0$, the value of the next iterate, $x^{(1)}$, rounded off to 2 decimal places, is ______

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: -0.01 to 0.01

Explanation

Here $f(1) = e - 5 = -2.2817$ and $f'(x) = e^x - 5$, so $f'(1) = -2.2817$. Then $x^{(1)} = 1 - \frac{-2.2817}{-2.2817} = 0$.