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AP EAMCET20228 Jul 2022Morning ShiftMathematicsLimitsActual

The integral value of n for which _ x 0 ( x-1) ( x-e^x ) x^n is a finite non zero real number is

Options

  1. A4
  2. B3
  3. C2
  4. D1

Correct answer

B. 3

Step-by-step solution

_ x 0 ( x-1) ( x-e^x ) x^n aligned & _ x 0 2 ^2 x / 2 (e^x-1+1- n ) x^n & _ x 0 1 2 [ (x / 2) x / 2 ]^2 (e^x-1+2 ^2 x / 2 ) x^ n-2 aligned It is non-zero if n -2=1 n =3

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