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JEE Main201815 Apr 2018Evening ShiftMathematicsLimitsActual

_ x 0 x 2 x-2 x x (1- 2 x)^2 equals.

Options

  1. A1
  2. B- 1 2
  3. C1 4
  4. D1 2

Correct answer

D. 1 2

Step-by-step solution

Let, aligned &L= _ x 0 (x 2 x-2 x x) (1- 2 x)^2 = _ x 0 K (say) & K= x [ 2 x 1-( x)^2 ]-2 x x (1- (1-2 ^2 x ) )^2 &= 2 x x- [2 x x-2 x ^3 x ] 4 ^4 x (1- ^2 x ) &= 2 x ^3 x 4 ^4 x (1- ^2 x ) &= 2 x ^3 x 4 ^4 x ( ^2 x- ^2 x ^2 x ) aligned aligned &= 2 x ^3 x ^3 x 4 ^4 x ( ^2 x- ^2 x ^2 x ) & K= x 2 x ( ^2 x- ^2 x ) x L &= _ x 0 x 2 x _ x 0 1 x ( ^2 x- ^2 x ) &= _ x 0 x 2 x _ x 0 1 0 ( ^2 0- ^2 0 ) &= 1 2 aligned

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