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AP EAMCET201920 Apr 2019Evening ShiftMathematicsBinomial TheoremActual

If x is so small that x^2 and higher powers of x can be neglected, then the approximate value of (1+ 3 4 x )^ 1 2 (1- 2 x 3 )⁻² is

Options

  1. A41+24 x 41
  2. B41-24 x 41
  3. C24+41 x 24
  4. D24-41 x 24

Correct answer

C. 24+41 x 24

Step-by-step solution

If x is so small that x^2 and higher powers of x can be neglected, then (1+x)^n=1+n x So, (1+ 3 4 x )^ 1 / 2 (1- 2 3 x )⁻²= (1+ 3 8 x ) (1+ 4 x 3 )=1+ 3 8 x+ 4 x 3 [on neglecting the x^2 term] = 24+41 x 24 Hence, option (c) is correct.

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