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GATE 2024 Chemical Engineering, Q50 · Numerical Methods

The correct answer is -0.01 to 0.01.

Question

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

Official answer: -0.01 to 0.01

Why

GATE 2024 official key: −0.01 to 0.01.f(1)=e−5≈−2.2817,0.01. f(1)=e−5\approx −2.2817, f'(x)=eˣ−5, f′(1)≈−2.2817.x(1)=1−(−2.2817)/(−2.2817)=1−1=0.00.f'(1)\approx −2.2817. x⁽¹⁾ = 1 − (−2.2817)/(−2.2817) = 1 − 1 = 0.00.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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