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JEE Main202524 Jan 2025Morning ShiftMathematicsLimitsActual

_ x 0 cosec x ( 2 ^2 x+3 x - ^2 x+ x+4 ) is:

Options

  1. A0
  2. B1 15
  3. C1 2 5
  4. D- 1 2 5

Correct answer

D. - 1 2 5

Step-by-step solution

aligned & _ x 0 cosec ( 2 ^2 x+3 x - ^2 x+ x+4 ) & _ x 0 ec x ( ^2 x+3 x- x-4 ) ( 2 ^2 x+3 x + ^2 x+ x+4 ) & _ x 0 1 x ( ^2 x+3 x-4 )- x ( 2 ^2 x+3 x + ^2 x+ x+4 ) & _ x 0 ( ^x+4 )( x-1)- x x ( 2 ^2 x+3 x + ^2 x+ x+4 ) & _ x 0 -2 ^2 x 2 ( x+4)-2 x 2 x 2 2 x 2 x 2 ( 2 ^2 x+3 x + ^2 x+ x+4 ) & _ x 0 - ( ^x( x+4)+ x 2 ) x 2 ( 2 ^2 x+3 x + ^2 x+ x+4 ) & - 1 2 5 aligned

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