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MHT CET202013 Oct 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= [ ( 4 +x ) ]^ 1 x if x 0=k if x=0 , is continuous at x=0 then k=

Options

  1. Ae
  2. Be
  3. Ce²
  4. De⁴

Correct answer

C. e²

Step-by-step solution

Given f(x) is continuous at x=0 _ x 0 [ ( 4 +x ) ]^ 1 x =K _ x 0 ( 1+ x 1- x )^ 1 x =K [ _ x 0 (1+ x)^ 1 x ]^ x x [ _ x 0 (1- x) -1 x ]^ x x = K [ _ x 0 (1+ x) 1 x ]^ _ x 0 x x [ _ x 0 (1- x) ]^ - _ x 0 x x =K e¹ e⁻¹ =K K=e²

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