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NDA2010MathematicsLimitsActual

What is _ x 0 a^x-b^x x equal to?

Options

  1. A(a b)
  2. Ba b
  3. C( a b )
  4. D( b a )

Correct answer

C. ( a b )

Step-by-step solution

aligned & _ x 0 a^x-b^x x & = _ x 0 a^x e^a-b^x e^b 1 aligned (using L'Hospital's Rule) aligned & = e^a- e^b & = ( a b ) aligned

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