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JEE Main20257 Apr 2025Morning ShiftMathematicsLimitsActual

_ x 0⁺ (5(x)^ 1 3 ) _e (1+3 x^2 ) ( ⁻¹ 3 x )^2 (e^ 5(x)^ 4 3 -1 ) is equal to

Options

  1. A1 15
  2. B1
  3. C1 3
  4. D5 3

Correct answer

C. 1 3

Step-by-step solution

aligned & _ x 0^ ( (5 x ^ 1 / 3 ) 5 x ^ 1 / 3 ) ( (3 x )^2 ( ⁻¹ 3 x )^2 ) ( (1+3 x ^2 ) 3 x ^2 ) ( 5 x ^ 4 / 3 e ^ 5 x^4 -1 ) 5 x ^ 1 / 3 3 x ^2 5 x ^ 4 / 3 9 x & = 1 3 aligned

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