Home
Class 12
MATHS
A function f(x) is defined as f(x)={(x^2...

A function `f(x)` is defined as `f(x)={(x^2-9)/(x-3);\ \ \ if\ x!=3\ \ \ 6;\ \ \ \ \ if\ x=3` Show that `f(x)` is continuous at `x=3` .

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

  • DEFINITE INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|562 Videos

Similar Questions

Explore conceptually related problems

A function f(x) is defined as f(x)={(x^2-x-6)/(x-3);\ \ \ if\ x!=3\ \ \ \ \ \ 5;\ \ \ \ \ \ \ if\ x=3 Show that f(x) is continuous at x=3 .

A function f(x) is defined as f(x)={(x^2 -x-6)/(x-3);ifx!=3 and 5ifx=3 Show that f(x) is continuous at x=3.

A function f(x) is defined as f(x) = -6x^(2) . What is f(-3) ?

The function f:R→R defined by f(x)=(x−1)(x−2)(x−3) is

If f(x) f(x) ={((x^2-9)/(x-3)","" " xne3),(" 6""," " "x = 3"):} then show that f(x) is continuous at x=3.

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is :

Find the relationship between ' a ' and ' b ' so that the function 'f' defined by f(x)={a x+1\ \ \ ,\ \ \ if\ xlt=3b x+3\ \ \ ,\ \ \ if\ x >3 is continuous at x=3 .

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

The function f is defined as f(x) = -4x^(3) - 4x^(2) . What is f(-4) ?

A function f :Rto R is defined as f (x) =3x ^(2) +1. then f ^(-1)(x) is :

RD SHARMA ENGLISH-CONTINUITY-All Questions
  1. Does there exists value of f(0) such that the following function becom...

    Text Solution

    |

  2. A function f(x) is defined as f(x)={(x^2-x-6)/(x-3);\ \ \ if\ x!=3\ \ ...

    Text Solution

    |

  3. A function f(x) is defined as f(x)={(x^2-9)/(x-3);\ \ \ if\ x!=3\ \ \ ...

    Text Solution

    |

  4. If f(x)={(x^2-1)/(x-1);\ for \ x!=1;\ \ \ 2\ for \ x=1 . Find wh...

    Text Solution

    |

  5. If f(x)={(sin3x)/x ,\ \ \ w h e n\ x!=0 1,\ \ \ w h e n\ x=0 . Find wh...

    Text Solution

    |

  6. If f(x)={e^(1//x),\ \ \ if\ x!=0 1,\ \ \ if\ x=0 . Find whether f is c...

    Text Solution

    |

  7. Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 ; 1,\ \ \ \ w h e n\ x=0 ...

    Text Solution

    |

  8. Show that f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 \ \ \ \ \ \ \ \ \ \ \ \ ...

    Text Solution

    |

  9. Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a \ \ \ \ \ \ \ \ \ \ ...

    Text Solution

    |

  10. Discuss the continuity of f(x)={|x|cos(1/x),\ \ \ x!=0 0,\ \ \ \ x=...

    Text Solution

    |

  11. Discuss the differentiability of f(x)={x^2sin(1/x),\ \ \ \ x!=0; 0 i...

    Text Solution

    |

  12. Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \...

    Text Solution

    |

  13. f(x)={(e^x-1)/(log(1+2x)),\ \ \ if\ x!=0\ \ \ \ \ \ \ \ \ 7,\ \ \ \ \...

    Text Solution

    |

  14. f(x)={(1-x^n)/(1-x),\ \ \( x!=1, (n-1) at x=1, n in N at x=1

    Text Solution

    |

  15. f(x)={(|x^2-1|)/(x-1),\ \ \ for x!=1 \ \ \ \ 2, for \ x=1 at x=1

    Text Solution

    |

  16. f(x)={(2|x|+x^2)/x ,\ \ \ x!=0 ,\ \ \ and 0 at x=0 is continuous at ...

    Text Solution

    |

  17. f(x)={|x-a|sin(1/(x-a)),\ \ \ for\ x!=a,\ \ \ 0\ \ \ if\ x=a at x=a

    Text Solution

    |

  18. Show that f(x)={1+x^2, if 0<=x<=1, 2-x,\ \ \ if\ x >1 is discontinu...

    Text Solution

    |

  19. Show that f(x)={(sin3x)/(tan2x),\ \ \ if\ x<0,\ 3/2,\ \ \ if\ x=0,\(lo...

    Text Solution

    |

  20. Find the value of ' a^(prime) for which the function f defined by f(x)...

    Text Solution

    |