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MHT CET202210 Aug 2022Morning ShiftMathematicsContinuity and DifferentiabilityActual

The function (f)(x)=[x]^2- [x^2 ] (where, [x] is the greatest integer less than or equal to x ), is discontinuous at

Options

  1. Aall integers.
  2. Ball integers except 0 .
  3. Call integers except 0 and 1 .
  4. Dall integers except 1 .

Correct answer

D. all integers except 1 .

Step-by-step solution

for x=0 . array l L.H.L = [O⁻ ]^2- [ (O⁻ )^2 ]=(-1)^2-(0)=1 R.H.L = [O⁺ ]^2- [O⁺ ]^2=0^2-(0)=0 array discount at x=0 for x=1 . array l L.H.L = [1⁻ ]^2- [ (1⁻ )^2 ]=0^2-0=0 R.H.L = [1⁺ ]^2- [ (1⁺ )^2 ]=1^2-1=0 F.V. =[1]^2- [1^2 ]=1-1=0 array continuous at x=1 the function f(x) is continuous at x=1 and discontinuous at all other integral point

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