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AP EAMCET202317 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

Let [t] represents the greatest integer not exceeding t and C =1-2 e ^2 . If the function f(x)= array cc [e^x ], & x < 0 a e^x+[x-2], & 0 x < 2 [e^ -x ]-C, & x 2 array . is continuous at x =2 , then f ( x ) is discontinuous at

Options

  1. Ax =1 only
  2. Bx=0 and x=1
  3. Cx=0 only
  4. Dx=0, x=1 and x= 1 2

Correct answer

A. x =1 only

Step-by-step solution

f(x) is continuous at x=2 aligned & LHL =f(2) & a e^2+[2-2]= [e⁻² ]- C & a e^2-1=0- (1-2 e^2 ) a=2 aligned

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