GATE 2025 BT – Question 33

Engineering Mathematics · Numerical Methods: Linear and nonlinear algebraic equations, trapezoidal and Simpson's rule, single step methods for ODEs · 1 mark · Numerical answer

Consider a nonlinear algebraic equation, $e^x - 2 = 0$. Using the Newton-Raphson method, with the initial guess of $x_0 = 1$, the approximated value of the root of the equation after one iteration is________. (Round off to two decimal places)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.73 to 0.75

Explanation

$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 1 - \frac{e - 2}{e} = 1 - 0.2642 = 0.74$.