Home
Class 12
MATHS
Show that the function f given by f(x)={...

Show that the function f given by `f(x)={x^3+3if""""x!=0 1if""""x=0` is not continuous at `x" "=" "0` .

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))|39 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(b) (LONG ANSWER TYPE QUESTIONS (I))|17 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

Similar Questions

Explore conceptually related problems

Show that the function f given by f(x)={x^(3)+3 if x!=0quad 1 if x=0 is not continuous at x=0

Show that the function f(x) given by f(x)={xsin1/x ,x!=0 0,x=0

Show that the function f(x) given by f(x)={(sin x)/(x)+cos x,x!=0 and 2,x=0 is continuous at x=0

Show that the functions f(x) given by f(x)={x(sin1)/(x),quad x!=00,quad x=0 is continuous at x=0

Show that the function 'f' given by : f(x)=|x|+|x-1|,x inR is continuous both at x = 0 and x = 1

Check the continuity of the function f given by f(x) = |x|at x = 0

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0 .

Show that the function f(x)=2x-|x| is continuous at x=0

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. Is the function defined by f(x)={x+5, ifxlt=1x-5, ifx >1 a continuous...

    Text Solution

    |

  2. Is the function f defined by f(x)={{:(x, if x le 1),(5, if x gt 1):...

    Text Solution

    |

  3. Show that the function f given by f(x)={x^3+3if""""x!=0 1if""""x=0 is ...

    Text Solution

    |

  4. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

    Text Solution

    |

  5. Discuss the continuity of the function : f(x)={{:(x",if "xge0),(x^(2...

    Text Solution

    |

  6. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

    Text Solution

    |

  7. Examine the continuity of the function : f(x)={{:(x+1" , "xle2),(2x-...

    Text Solution

    |

  8. f(x)={{:((x^(2)-25)/(x-5)",","when",x ne 5),( 10",", "when",x=5):} is ...

    Text Solution

    |

  9. Discuss the continuity of the function : f(x)={{:((|x-2|)/(x-2)", "x...

    Text Solution

    |

  10. Discuss the continuity of the function : f(x)={{:((|x-2|)/(2-x)", "x...

    Text Solution

    |

  11. Discuss the continuity of the function : f(x)={{:((|x-a|)/(x-a)",whe...

    Text Solution

    |

  12. Discuss the continuity of the function f, where f is defined by f(x){{...

    Text Solution

    |

  13. Discuss the continuity of the function f, where f is defined byf(x)={...

    Text Solution

    |

  14. Discuss the continuity of the function : f(x)={{:(x", "0lexlt1/2),(...

    Text Solution

    |

  15. Discuss the continuity of the function : f(x)={{:((1-cosx)/x^(2)", "...

    Text Solution

    |

  16. Show that the function f(x)defined as f(x) = xcos(1/x),x!=0; 0,x=0is c...

    Text Solution

    |

  17. Show that the following functions are continuous at x = 0 : f(x)={{:...

    Text Solution

    |

  18. Test the continuity of the function f (x) : f(x)={{:(x^(2)sin.(1)/(...

    Text Solution

    |

  19. f(x)={{:(cosx",","when",x ge0, ),(-cosx",", "when", x lt0):} is discon...

    Text Solution

    |

  20. Examine the continuity of the function f(x) at x = 0. f(x)={{:(sinx/...

    Text Solution

    |