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MHT CET20255 May 2025Evening ShiftMathematicsApplication of DerivativesActual

The approximate value of 1 (2 002)^2 is

Options

  1. A0.2495
  2. B0.2595
  3. C0.2095
  4. D0.2392

Correct answer

A. 0.2495

Step-by-step solution

The approximate value of 1 (2.002)^2 is found using differential approximation with f(x) = x⁻² . Let x₀ = 2 and x = 0.002 , so f(2) = 0.25 and f'(x) = -2x⁻³ , giving f'(2) = -0.25 . The linear approximation yields f(2.002) f(2) + f'(2) x = 0.25 - 0.25 0.002 = 0.2495 . Comparing with the choices, the approximation matches option A .

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