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MHT CET202012 Oct 2020Evening ShiftMathematicsContinuity and DifferentiabilityActual

If f(x)= (e^ 2 x -1 ) x⁰ x² , x 0 is continuous at x=0 , then f(0)=

Options

  1. A90
  2. B180
  3. C90
  4. D180

Correct answer

C. 90

Step-by-step solution

aligned f (0) &= _ x 0 ( e ^ 2 x -1 ) x 180 x ² [ x^ = ( x 180 )^ c ] &= _ x 0 ( e ^ 2 x -1 x ) ( x 180 x ) &= (2 _ x 0 e ^ 2 x -1 2 x ) 180 [ _ x 0 x 180 x 180 ]=2( e ) ( 180 )= 90 aligned

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