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AP EAMCET201920 Apr 2019Morning ShiftMathematicsLimitsActual

If ( _ x x^3+1 x^2+1 -( x+ ) ) exists and equal to 2 , then the ordered pair (( , ) ) of real numbers is

Options

  1. A((1,-1) )
  2. B((-2,1) )
  3. C((-1,1) )
  4. D((1,-2) )

Correct answer

D. ((1,-2) )

Step-by-step solution

It is given that, ( aligned & _ x x^3+1 x^2+1 -( x+ ) =2 & _ x x^3+1- x^3- x^2- x- x^2+1 =2 aligned ) For the existance of limit, coefficient of (x^3=0 ) ( aligned & =1 & _ x - x^2-x- +1 x^2+1 =2 & _ x - - 1 x - x^2 + 1 x^2 1+ 1 x^2 =2 - =2 =-2 & ( , )=(1,-2) aligned ) Hence, option (4) is correct.

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