AP EAMCET202318 May 2023Morning ShiftMathematicsLimitsActual
Which one of the following function is discontinuous at x =1 ?
Options
- Af(x)= ^2 x+ ^2 x+ ^2 x- ^2 x
- Bf(x)= 1 1+2^ x
- Cf(x)= cases x-1 |x-1|+2(x-1)^2 , & x 1 1, & x=1 cases
- Df(x)=e^x+5
Correct answer
C. f(x)= cases x-1 |x-1|+2(x-1)^2 , & x 1 1, & x=1 cases
Step-by-step solution
f(x)= array cc x-1 |x-1|+2(x-1)^2 & x 1 1 & x=1 array . f(x)= array cc 1 2 x-1 & x>1 1 2 x-3 & x < 1 1 & x=1 array . aligned & _ x 1⁺ +f(x)= _ h 0 1 2(1+h)-3 = _ h 0 1 2 h-1 =-1 & and f(1)=1 aligned _ x 1⁺ f(x) f(1) f ( x ) is not continuous on x =1 .