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AP EAMCET2013MathematicsBinomial Theorem

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

Options

  1. A1-2 x
  2. B1-3 x
  3. C1-4 x
  4. D1-5 x

Correct answer

A. 1-2 x

Step-by-step solution

Given expression is aligned & E= (1-2 x)⁻¹(1-3 x)⁻² (1-4 x)⁻³ &= (1+2 x+2 x^2+ )(1+6 x+ ) (1+12 x+ ) &= (1+2 x+6 x+ ) (1+12 x) &=(1+8 x)(1+12 x)⁻¹ &=(1+8 x)(1-12 x ) &=(1+8 x-12 x ) &=(1-4 x) & ( neglecting the higher term ) aligned ( neglecting the higher term)

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