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SSC Applied Mathematics QUESTION #1309
Question 1
For \(f(x)=x-\cos x\), the derivative \(f'(x)\) used in Newton-Raphson is:
  • \(1+\sin x\)✔️
  • \(1-\sin x\)
  • \(-\sin x\)
  • \(\cos x\)
Correct Answer Explanation
\(f(x)=x-\cos x\Rightarrow f'(x)=1+\sin x\). The Newton-Raphson iteration becomes: \(x_{n+1}=x_n-\dfrac{x_n-\cos x_n}{1+\sin x_n}\). Starting near \(x=\pi/4\approx0.7854\) converges to the root \(\approx0.7391\).