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AP EAMCET202021 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

By neglecting (x^4 ) and higher powers of (x ), find approximate value of ( [3] x^2+64 - [3] x^2+27 )

Options

  1. A(1- 7 234 x^2 )
  2. B(1- 7 432 x^2 )
  3. C(1- 7 32 x^2 )
  4. D(1- 7 42 x^2 )

Correct answer

B. (1- 7 432 x^2 )

Step-by-step solution

Given expression ( aligned [3] x^2+64 - [3] x^2+27 & =4 (1+ x^2 64 )^ 1 / 3 -3 (1+ x^2 27 )^ 1 / 3 & =4 [1+ x^2 3 64 ]-3 [1+ x^2 3 27 ] aligned ) on neglecting (x^4 ) and higher powers of (x ) ( aligned & =4+ x^2 48 -3- x^2 27 =1+ 27-48 48 27 x^2 & =1- 21 48 27 x^2=1- 7 432 x^2 aligned ) Hence, option (b) is correct.

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