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AP EAMCET2003MathematicsLimits

If a>0, _ x a a^x-x^a x^x-a^a =-1 , then a is equal to

Options

  1. A0
  2. B1
  3. Ce
  4. D2 e

Correct answer

B. 1

Step-by-step solution

We have, _ x a a^x-x^a x^x-a^a =-1 Using L^ hospital's rule _ x a a^x a-a x^ a-1 x^x(1+ x) =-1 a^a a-a a^ a-1 a^a(1+ a) =-1 a-1=-1- a 2 _e a=0 a=e^0=1

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