Home
Class 12
MATHS
If f(x)= {:{((x^(2)-4)/(x-2)", for " x!=...

If `f(x)= {:{((x^(2)-4)/(x-2)", for " x!=2),(5", for " x=2):}`, then at `x=2`

A

f is continuous if `f(0)=-2`

B

f is continuous

C

f has removable discontinuity

D

f has irremovable discontinuity

Text Solution

Verified by Experts

The correct Answer is:
C
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

f(x) = {{:((2x^(2)-3x-2)/(x-2), if x ne 2), (5, if x = 2):} at x = 2 .

If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x^(2)-5", for " 4 lt x le 6):} , then

If f(x)={((2x+5)/(x+1)", for " 0 le x lt 2),(4x-5", for " 2 le x le 4),((x^(2)+2)/(x-5)", for " 4 lt x le 6"," x !=5):} then

If (x)=(x^(2)-4)-:(x-2) f o rx <2,f(x)=4 for x=2 and f(x)=2 for x<2, then f(x) at x=2 is

If f(x) (2^(x+2)-16)/(4^(x)-2^(4)), x != 2 is continuous at x = 2 , then the value of f(2) is

if f(x)={[x^(3)+x^(2), for 0<=x<=2x+2, for 2

If f(x)=max{x^(2)-4,|x-2|,|x-4|} then:

If f(x) {:(=-x^(2)", if " x le 0 ), (= 5x - 4 ", if " 0 lt x le 1 ),(= 4x^(2)-3x", if " 1 lt x le 2 ):} then f is

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x) is continuous at x=0, where f(x)={:{((1+3x)^(1/x)", for " x !...

    Text Solution

    |

  2. If f(x) is continuous at x=0, where f(x)=((4-3x)/(4))^(8/x)", for " x...

    Text Solution

    |

  3. If f(x)= {:{((x^(2)-4)/(x-2)", for " x!=2),(5", for " x=2):}, then at ...

    Text Solution

    |

  4. If f(x)={:{(root(3)((4x+1)/(1-4x))", for " x!=0),(e^(6)", for " x=0):}...

    Text Solution

    |

  5. If f(x) is continuous at x=0, where f(x)=((4-3x)/(4+5x))^(1/x)", for ...

    Text Solution

    |

  6. If f(x) is continuous at x=2, where f(x)=(x-1)^((1)/(2-x)), for x!=2, ...

    Text Solution

    |

  7. If f(x) is continuous at x=0, where f(x)={:{((sec^(2)x)^(cot^(2)x)", ...

    Text Solution

    |

  8. If f(x) is continuous at x=pi/4, where f(x)=(1+cos 2x)^(4sec 2x), for ...

    Text Solution

    |

  9. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

    Text Solution

    |

  10. f(x) = {{:(("tan"(pi)/(4)+x)^(1//x)",",x ne 0),(k",",x = 0):} for what...

    Text Solution

    |

  11. The function f(x)=(sin 2x)^(tan^(2)2x) is not defined at x=(pi)/(4). T...

    Text Solution

    |

  12. If f(x) is continuous at x=1, where f(x)=(log(2)2x)^(1/(log(2)x), for ...

    Text Solution

    |

  13. If f(x) is continuous at x=0, where f(x)={:{((8^(x)-2^(x))/(k^(x)-1)"...

    Text Solution

    |

  14. If f(x) is continuous at x=0, where f(x)=(4^(x)-e^(x))/(6^(x)-1), for...

    Text Solution

    |

  15. The value of f at x =0 so that funcation f(x) = (2^(x) -2^(-x))/x , ...

    Text Solution

    |

  16. If the function f(x) defined by f(x)={(log(1+a x)-log(1-b x))/x ,\ \ \...

    Text Solution

    |

  17. If f(x) is continuous at x=0, where f(x)=(log 100 + log (0.01 +x))/(...

    Text Solution

    |

  18. For what value of k , the function defined by f(x) =(log (1+2x)...

    Text Solution

    |

  19. If f(x)={(log((1-3x))(1+3x)",","for",x ne 0),(k",","for",x =0):} is co...

    Text Solution

    |

  20. If f(x) is continuous at x=7, where f(x)=(log x-log 7)/(x-7), for x!=7...

    Text Solution

    |