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MHT CET202520 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

The approximate value of (59^ 30^ ) is (given 1^ =0.0175^ c , 60^ =0.8660 )

Options

  1. A0.5076
  2. B0.5176
  3. C0.5256
  4. D0.5150

Correct answer

A. 0.5076

Step-by-step solution

The approximation for (59^ 30') uses linear approximation with f(x) = x , giving f(x₀ + x) f(x₀) + f'(x₀) x . With x₀ = 60^ and x = -30' = -0.5^ , convert x to radians using 1^ = 0.0175^ c , so x = -0.5 0.0175 = -0.00875^ c . Given (60^ ) = 0.5 and (60^ ) = 0.8660 , then f'(x₀) = - (60^ ) = -0.8660 . Substitute into the approximation: (59^ 30') 0.5 + (-0.8660)(-0.00875) = 0.5 + 0.0075775 = 0.5075775 . Rounded to four decimal places, this yields 0.5076 , matching option A .

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