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COMEDK2022MathematicsBinomial Theorem

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 . We want to find the approximate value of (0.007)^ 1/3 . Consider x = 0.008 and x = -0.001 . Then x + x = 0.007 . Using the linear approximation formula f(x + x) f(x) + f'(x) x , we have f'(x) = 1 3 x^ -2/3 = 1 3 x^ 2/3 . For x = 0.008 , f(0.008) = (0.008)^ 1/3 = 0.2 . f'(0.008) = 1 3 (0.008)^ 2/3 = 1 3 (0.2)^2 = 1 3 0.04 = 1 0.12 = 100 12 = 25 3 . Substituting these values into the approximation formula: (0.007)^ 1/3 0.2 + ( 25 3 ) (-0.001) = 0.2 - 0.025 3 = 0.6 - 0.025 3 = 0.575 3 = 575 3000 .

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