GATE_AE_2027_MOCK_03_Q39 GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories) NAT · 2 Marks
Engineering Mathematics • Numerical Methods • Newton-Raphson Method

To find the root of f(x) = x^2 - 5 = 0 using the Newton-Raphson method starting with initial guess x_0 = 2.0, what is the value of x_1 after the first iteration? (Round off to two decimal places).

Answer Key:
2.25

Step-by-Step Verified Solution

### Solution: x_1 = x_0 - f(x_0)/f'(x_0). f(2) = 2^2 - 5 = -1. f'(x) = 2x ==> f'(2) = 4. x_1 = 2 - (-1)/4 = 2 + 0.25 = 2.25. Correct: 2.25.
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