Home
Class 12
MATHS
Discuss the continuity of the function f...

Discuss the continuity of the function f, where f is defined by `f(x){{:(3"," if 0 le x le 1),(4"," if 1lt x lt 3 ),(5"," if 3 le x le 10):}`

Text Solution

Verified by Experts

The correct Answer is:
Discontinuous at x = 1, 3
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

If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 le x le 10):} , then

The points of discontinuity of the function f (x) = {{:(3x + 1"," ,0 le x lt2),(4x - 1"," ,2 lt x le 6),(5x + 2",", 6 lt x le 10 ):} are:

If f(x)={:{(3x+5", for " 0 le x lt 3),(2x+8", for " 3 le x lt 5),(x+13", for " 5 le x le 10):} , then

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

Let f:R to R be a function defined as f(x)={{:(5,"if" x le 1),(a+bx , "if" 1 lt x lt 3),(b+5x , "if" 3 le x lt 5),(30 , "if" x ge 5):} then f is

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

Examine the continuity of the following function at x = 1 f(x) = {(x+2,-1 le x lt1),(4-x,1 le x):}

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)
  1. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Examine the continuity of the funcation f(x)={{: ((|sinx|)/x",", xne...

    Text Solution

    |

  19. Examine the continuity of the function f(x) at x = 0. f(x)={{:((tan2...

    Text Solution

    |

  20. Discuss the continuity of the cosine, cosecant, secant and cotangen...

    Text Solution

    |