Home
Class 12
MATHS
Consider the function f(x) = [{:(x{x}+1"...

Consider the function `f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):}`, where {x} denotes the fractional part function. Which one of the following statements is not correct ?

A

`underset(x rarr 1)(lim) f(x)` exists

B

`f(0) ne f(2)`

C

f(x) is continuous in [0, 2]

D

Rolle's theorem is not applicable to f(x) in [0, 2]

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The number of points for x in [-2,2] where f (x) is non-differentiable is:

If f(x)={:{(x", for " 0 le x lt 1/2),(1-x", for " 1/2 le x lt 1):} , then

Consider a function defined in [-2,2] f (x)={{:({x}, -2 lle x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is:

Consider the function f(x)=[x{x}+1,0<=x<1 and 2-{x},1<=x<=2 Which of the following statement is/are correct? {x} denotes the fractional part function.

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

If f(x)={:{(x-1", for " 1 le x lt 2),(2x+3", for " 2 le x le 3):} , then at x=2

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then

If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x le 2):} , then f is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)

    Text Solution

    |

  2. If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, t...

    Text Solution

    |

  3. Consider the function f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  4. Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  5. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  6. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  7. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  8. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  9. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

    Text Solution

    |

  10. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  11. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  12. The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...

    Text Solution

    |

  13. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  14. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...

    Text Solution

    |

  15. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...

    Text Solution

    |

  16. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  17. Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...

    Text Solution

    |

  18. If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then

    Text Solution

    |

  19. Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...

    Text Solution

    |

  20. Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...

    Text Solution

    |