Home
Class 12
MATHS
If f(x)={:{(2x", if " x lt 2),(2", if " ...

If `f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):}`, then

A

`underset( x rarr 2^(-))lim f(x)=-4`

B

`underset(x rarr 2^(+))lim f(x)=-4`

C

f has irremovable discontinuity

D

f has removable discontinuity

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    NIKITA PUBLICATION|Exercise MCQS|77 Videos

  • DEFINITE INTEGRAL

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|243 Videos

Similar Questions

Explore conceptually related problems

At x = 0 , f(x) {:(=x-2", if " x lt 0 ),(= 1//2", if " x = 0 ),(=x^(2)", if " x gt 0 ):}} is

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

If f(x) {:(= 2x - 1 ", if " x gt 2 ),(= 2k ", if " x = 2 ), (=x^(2)-1", if " x lt 2 ) :} is continuous on R , then k = …….

Draw the graph of the function: f(x) = {(x," if " x le 0),(x^(2)," if " 0 lt x le 2),(x," if " x gt 2):}

f(x) {{:(-2"," if x le -1),(2x"," if -1lt x le 1),(2"," if x gt 1):}

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

If {(5/2,",", x lt 2),(1,",",x = 2),(x-3/2,",",x gt 2):} , then

If f(x) is continuous at x=2 , where f(x)={:{(4x-3", for " x lt 2),(kx+7", for " x gt 2):} , then k=

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x) is continuous at x=0, where f(x)={((sin x)/(x)+cos x", for " ...

    Text Solution

    |

  2. If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):}, then

    Text Solution

    |

  3. If f(x)={:{(2x", if " x lt 2),(2", if " x=2),(x^(2)", if " x gt2):}, t...

    Text Solution

    |

  4. If f(x)={:{(x-1", for " 1 le x lt 2),(2", for " x=2),(2x-3", for " 2 l...

    Text Solution

    |

  5. If f(x)={:{(x^(2)", for " x le 1),(x+3", for " x gt 1):}, then at x=1

    Text Solution

    |

  6. If f(x)=sqrt(x-2), for 2 lt x lt 4, then f(x) is

    Text Solution

    |

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

    Text Solution

    |

  8. If f(x)={:{(3x+5", for " 0 le x lt 3),(2x+8", for " 3 le x lt 5),(x+13...

    Text Solution

    |

  9. If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):}, then

    Text Solution

    |

  10. If f(x)={((2x+5)/(x+1)", for " 0 le x lt 2),(4x-5", for " 2 le x le 4)...

    Text Solution

    |

  11. If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...

    Text Solution

    |

  12. If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...

    Text Solution

    |

  13. If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is

    Text Solution

    |

  14. If f(x)=(x+1)/((x-2)(x-5)), then in [4, 6]

    Text Solution

    |

  15. If f(x)=(x+1)/((x-2)(x-5)), then in [0, 1]

    Text Solution

    |

  16. If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is

    Text Solution

    |

  17. If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...

    Text Solution

    |

  18. If f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x l...

    Text Solution

    |

  19. If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 l...

    Text Solution

    |

  20. If f(x)={:{(-2", for " x le -1),(2x", for " -1 lt x le 1),(2", for " x...

    Text Solution

    |