Home
Class 12
MATHS
If f(x) is continuous at x=0, where f(...

If `f(x)` is continuous at `x=0`, where `f(x)=(log 100 + log (0.01 +x))/(3x)` , for `x!=0`, then `f(0)=`

A

`(10)/(3)`

B

`(100)/(3)`

C

`1/3`

D

100

Text Solution

Verified by Experts

The correct Answer is:
B
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

If f(x) is continuous at x=0 , where f(x)=(log(1+x+x^(2))+log(1-x+x^(2)))/(sin x) , for x!=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=(log(2+x)-log(2-x))/(tan x) , for x!=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=(log(1+x^(2))-log(1-x^(2)))/(sec x- cos x) , for x !=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=((3^(sin x)-1)^(2))/(x log (1-x)) , for x!=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=((4^(sin x)-1)^(2))/(x log (1+2x)) , for x!=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=((e^(3x)-1)sin x^(@))/(x^(2)) , for x!=0 , then f(0)=

If f(x) is continuous at x=0 , where f(x)=(sqrt(1+x)-root3(1+x))/(x) , for x!=0 , then f(0)=

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

If f(x) is continuous at x=0 , where f(x)=(log sec^(2)x)/(x sin x) , for x!= 0 then f(0)=

If f(x) is continuous at x=0 , where f(x)={:{((log (1+kx))/(sin x)", for " x!=0),(5", for " x=0):} , then k=

NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. The value of f at x =0 so that funcation f(x) = (2^(x) -2^(-x))/x , ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. If f(x) is continuous at x=0, where f(x)=(e^(5x)-e^(2x))/(sin 3x), for...

    Text Solution

    |

  8. Let f(x)=((e^(kx)-1).sinKx)/x^2 for x!=0;=4, for x=0 is continuous at ...

    Text Solution

    |

  9. If f(x) is continuous at x=0, where f(x)=((e^(2x)-1)tan x)/( x sin x)...

    Text Solution

    |

  10. If f(x) is continuous at x=0, where f(x)=((e^(3x)-1)sin x^(@))/(x^(2))...

    Text Solution

    |

  11. if f(x)=(e^(x^(2))-cosx)/(x^(2)), for xne0 is continuous at x=0, then ...

    Text Solution

    |

  12. If f(x) is continuous at x=0, where f(x)={:{((3^(x)-3^(-x))/(sin x)",...

    Text Solution

    |

  13. If f(x) is continuous at x=0, where f(x)={:{((9^(x)-9^(-x))/(sin x)"...

    Text Solution

    |

  14. If f(x) is continuous at x=0, where f(x)=(10^(x)+7^(x)-14^(x)-5^(x))/...

    Text Solution

    |

  15. If f(x) is continuous at x=0, where f(x)=((5^(x)-2^(x))x)/(cos 5x-cos...

    Text Solution

    |

  16. If f(x) is continuous at x=0, where f(x)=(4^(x)-2^(x+1)+1)/(1-cos x),...

    Text Solution

    |

  17. If f(x) is continuous at x=pi/2, where f(x)=(3^(x- pi/2)-6^(x- pi/2))...

    Text Solution

    |

  18. If f(x) is continuous at x=a,a>0, where f(x)=[(a^x-x^a)/(x^x-a^a), for...

    Text Solution

    |

  19. The function f(x) is condtions at the point x=0 where f(x)=log(1+kx)...

    Text Solution

    |

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

    Text Solution

    |