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MHT CET202615 April 2026Evening ShiftMathematicsBinomial TheoremActual

The approximate value of (0.007)^ 1 3 is

Options

  1. A21 120
  2. B23 120
  3. C29 120
  4. D31 120

Correct answer

B. 23 120

Step-by-step solution

Let f(x) = x^ 1 3 Let x = 0.008 and x = -0.001 f(x) = (0.008)^ 1 3 = 0.2 = 1 5 f'(x) = 1 3 x^ - 2 3 f'(0.008) = 1 3(0.008)^ 2 3 = 1 3(0.04) = 1 0.12 = 100 12 = 25 3 Using the approximation f(x + x) f(x) + f'(x) x f(0.007) 1 5 + ( 25 3 )(-0.001) f(0.007) 1 5 - 25 3000 f(0.007) 1 5 - 1 120 f(0.007) 24 - 1 120 = 23 120 Answer: 23 120

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