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JEE Main2003MathematicsLimitsActual

Let f ( a )= g ( a )= k and their n th derivatives f ^ n ( a ), g ^ n ( a ) exist and are not equal for some n . Further if _ x a f(a) g(x)-f(a)-g(a) f(x)+f(a) g(x)-f(x) =4 then the value of k is

Options

  1. A0
  2. B4
  3. C2
  4. D1

Correct answer

B. 4

Step-by-step solution

_ x a k 9(x)-k f(x) 9(k)-f(x) =4 (By L'Hospital rule) _ x a k 9^ (x)-f^ (x) 9^ (x)-f^ (x) =4 or k=4

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