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JEE Advanced2024MathematicsLimitsActual

Let k R . If _ x 0^+ ( ( k x)+ x+x)^ 2 x =e^6 , then the value of k is

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

B. 2

Step-by-step solution

( aligned & l= _ x 0⁺ ( ( k x)+ x+x)^ 2 x =e^6 & l= _ x 0⁺ 2 x ( ( k x)+ x+x-1) & l= _ x 0⁺ 2 ( ( k x) k x k x k x k x x +1- (1- x) x^2 x ) & l=2(k+1) & l=e^ 2(k+1) =e^6 & k+1=3 & k=2 aligned )

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