Home
Class 12
MATHS
Show that the function f(x) ={:{((sin 3x...

Show that the function `f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " x= 0):},` is discontinuous at x=0.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5b|7 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Exercies 5c|14 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x)={{:(x/|x|",", " when ", x ne0),(1",", " when ", x =0):} is discontinuous at x=0

f(x)={{:((sin3x)/(x)",","when",x ne0 ),( 1",", "when",x=0):} is discontinuous atx =0.

If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then discuss its continuity at x= 0. .

The function f(x) = [{:(sin(ln |x|), x ne 0),(1, x=0):}

Show that the funcation f(x)={{:(3x-2",", " when ", x le0),(x+1",", " when ", x gt 0):} is discontinuous at x =0

If f(x)={(x^(k) sin((1)/(x))",",x ne 0),(0",", x =0):} is continuous at x = 0, then

Show that the function defined by f(x) = {{:(x^(2) sin 1//x",",x ne 0),(0",",x = 0):} is differentiable for every value of x, but the derivative is not continuous for x =

Let f(x) = {:{ (x sin""(1/x) , x ne 0) , ( k , x = 0):} then f(x) is continuous at x = 0 if

NAGEEN PRAKASHAN-Continuity and Differentiability-Exercies 5a
  1. Discuss the continuiy of the function f(x)={(1/x ", " x ne 0),(1...

    Text Solution

    |

  2. Discuss the continuity of the function f(x)={((|x|)/x", " xne 0)...

    Text Solution

    |

  3. (i) Dissusse the continuity of the function f(x)={(|x-a|", " xne a...

    Text Solution

    |

  4. Show that f(x) = sinx is continuous for all values of x.

    Text Solution

    |

  5. Prove that f(x) = {sinx/x ; x != 0 and 1 ; x=0. is continuous at x=0...

    Text Solution

    |

  6. If f(x) ={:{((sin 3x)/(sin 5x)", "x ne 0),(0", " x= 0):}, then d...

    Text Solution

    |

  7. Show that the function f(x) ={:{((sin 3x)/(x)", "x ne 0),(1", " ...

    Text Solution

    |

  8. Discuss the continuity of f(x) ={:{((sin^2 2x)/(x^2)", "x ne 0),(1", ...

    Text Solution

    |

  9. Discuss the continuity of f(x) ={:{(cos""(1)/(x)", "x ne 0),(" "1",...

    Text Solution

    |

  10. Discuss the continuity of f(x) ={:{(sin""(1)/(x)", "x ne 0),(" "1", ...

    Text Solution

    |

  11. Discuss the continutiy of f(x) ={:{(xcos""(1)/(x)", "x ne 0),(" "0...

    Text Solution

    |

  12. Disuss the continutiy of f(x) ={:{((sin^2 x)/(x^2)", "x ne 0),(" "0"...

    Text Solution

    |

  13. If the function f(x) ={:{((3x^3-2x^2-1)/(x-1)", "x ne 1),(" "K", ...

    Text Solution

    |

  14. For what value of k, the function f(x) ={:{(Kx^2", " x le 2 ),(" ...

    Text Solution

    |

  15. For what value of k, the function f(x) ={:{((x^2-4)/(x-2)", " x ne 2...

    Text Solution

    |

  16. For what value of k, the function f(x) ={:{(2x+1", "x gt2),(" ...

    Text Solution

    |

  17. If the function f(x) given by f(x)={(3a x+b,"if "x >1), (11,"if "x=1),...

    Text Solution

    |

  18. Discuss the continuity of the function f(x) ={:{((1+cos x)/(tan^2 x...

    Text Solution

    |

  19. Discuss the continuity of the function f(x) ={:{((Sinx)/(x) ", "x ...

    Text Solution

    |

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

    Text Solution

    |