GATE 2016 CE (CE1) – Question 11
Use Newton–Raphson to solve $3x-e^x+\sin x=0$. With initial estimate $x_0=0.333$, the next estimate, correct to three decimal places, is ______.
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Correct answer: 0.355 to 0.365
Explanation
For f(x)=3x−exp(x)+sin(x), f-prime(x)=3−exp(x)+cos(x). Newton iteration is x1=x0−f(x0)/f-prime(x0). Substituting x0=0.333 gives x1≈0.3602, or **0.360** to three decimals. This is one iteration, rather than the fully converged root.