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Manipal MET2014MathematicsLimits

The value of the _ x 0 ( a^x+b^x+c^x 3 )^ 2 / x , (a, b, c 0) is

Options

  1. A(a b c)^3
  2. Babc
  3. C(a b c)^ 1 / 3
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

aligned & Let y= _ x 10 ( a^x+b^x+c^x 3 )^ 2 / x & array l y= _ x 10 2 x ( a^x+b^x+c^x 3 ) = _ x 10 (a^x+b^x+c^x )- 3 x y= (a b c)^ 2 / 3 (by L-Hospital's rule) y=(a b c)^ 2 / 3 array aligned

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