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COMEDK2023MathematicsLimits

The value of _ x ( x^2-2 x+1 x^2-4 x+2 )^ 2 x is

Options

  1. Ae^2
  2. Be^4
  3. Ce
  4. De¹⁶

Correct answer

B. e^4

Step-by-step solution

aligned & Let L= _ x ( x^2-2 x+1 x^2-4 x+2 )^ 2 x & L= _ x [2 x ( x^2-2 x+1 x^2-4 x+2 ) ] & L= _ x [2 x (1+ 2 x-1 x^2-4 x+2 ) ] & L= _ x [2 x ( 2 x-1 x^2-4 x+2 - ( 2 x-1 x^2-4 x+2 )^2 2 + . . & .+ ( 2 x-1 x^2-4 x+2 )^3 3 ) . aligned aligned & L= ( _ x 2 x(2 x-1) x^2-4 x+2 )-0+0 . & L= _ x 4 x^2 (1- 1 2 x ) x^2 (1- 4 x + 2 x ) & L= 4(1-0) (1-0+0) & L=4 & L=e^4 aligned

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