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AP EAMCET202017 Sep 2020Morning ShiftMathematicsBinomial TheoremActual

Assuming (|x| ) to be so small, that (x^2 ) and higher powers of (x ) can be neglected, then ( 1+x +(1-x)^ 3 / 2 (1+x)+ 1+x = )

Options

  1. A(1+ 5 x 4 )
  2. B(1- 5 x 4 )
  3. C(1+ 4 x 5 )
  4. D(1- 4 x 5 )

Correct answer

B. (1- 5 x 4 )

Step-by-step solution

Given, (|x| ) is very small, (x^2 ) is negligible ( aligned & 1+x +(1-x)^ 3 / 2 (1+x)+ 1+x = 1+ 1 2 x+1- 3 2 x 1+x+1+ x 2 & = 2-x 2+ 3 x 2 = 4-2 x 4+3 x = (4-2 x)(4-3 x) (16-9 x^2 ) & = 16-20 x+6 x^2 16-9 x^2 = 16-20 x 16 x^2 negligible & =1- 5 x 4 aligned )

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