GATE 2026 BM – Question 39
Engineering Mathematics · Numerical Methods · 2 marks · Multiple choice
Use Newton–Raphson to solve $x=e^{-2x}$ starting from x0=0. Find the first iterate x1.
- 1
- 1/2
- 1/3
- 1/4
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Show answer and explanation
Correct answer: (C) 1/3
Explanation
Write f(x)=x−e⁻²ˣ, so f′(x)=1+2e⁻²ˣ. At zero, f=−1 and f′=3. Newton’s update gives $x_1=x_0-f(x_0)/f\prime(x_0)=0-(-1)/3=1/3$. Thus C.
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