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MHT CET202015 Oct 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

If the function given by f(x)= ( 4 x+1 1-4 x )^ 1 x for x o is continuous at x=0 , then the value of f ( o ) is

Options

  1. Ae ⁸
  2. Be ¹⁰
  3. Ce ⁻⁸
  4. De ⁻¹⁰

Correct answer

A. e ⁸

Step-by-step solution

aligned _ x 0 ( 1+4 x 1-4 x )^ 1 x &= _ x 0 (1+4 x)^ 1 x _ x 0 (1-4 x)^ 1 x = [ _ x 0 (1+4 x)^ 1 4 x ]⁴ [ _ x 0 (1-4 x)^ -1 4 x ]⁻⁴ = e⁴ e⁻⁴ &=e⁸ aligned

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