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GATE 2019 ME (ME2) – Question 38

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 2 marks · Multiple choice

Estimate the derivative of $f(x)=\cos x$ by $f^\prime(x)\approx[f(x+h)-f(x-h)]/(2h)$. Percentage error is [(exact − approximate)/exact] × 100. At $x=\pi/6$ rad and h = 0.1 rad, which interval contains the error?

  1. < 0.1%
  2. > 0.1% and < 1%
  3. > 1% and < 5%
  4. > 5%

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Show answer and explanation

Correct answer: (B) > 0.1% and < 1%

Explanation

The centred difference is $-\sin x\,(\sin h/h)$ and exact derivative is $-\sin x$. Percentage error is $[1-\sin(0.1)/0.1]100=0.166583\%$. Thus it is above 0.1% and below 1%. **B**.