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GATE 2022 AG – Question 21

Engineering Mathematics · Numerical Methods · 1 mark · Numerical answer

For $\sin x-4x+1=0$, use Newton–Raphson once from $x_0=.2$. Give the next estimate to three decimals.

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Correct answer: 0.250 to 0.350

Explanation

$f(.2)=\sin(.2)-.8+1=.3986693$ and $f^{\prime}(.2)=\cos(.2)-4=-3.0199334$. Thus $x_1=.2-.3986693/(-3.0199334)=.3320126$, giving **.332**. Trigonometric arguments are in radians.

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