Home
Class 12
MATHS
Test the continuity of the function f (x...

Test the continuity of the function f (x) :
`f(x)={{:(x^(2)sin.(1)/(x),"when " xne0),(0,"when " x=0):}`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)" is continuous for all "x"inRR`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( Multiple Choice Type Questions)|2 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( Very Short Answer Type Questions)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise EXERCISE 2A ( short Answer Type Questions)|8 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

Similar Questions

Explore conceptually related problems

Examine the continuity of the function f(x)={{:((|"sin"x|)/(x),"when " xne0),(" 1","when "x=0):}

Examine the continuity of the following function at x = 0 : phi(x)={{:(|2x|/(x)," when " xne0),(0,"when " x=0):}

Examine the continutiy of f (x) at x= 1 , where f(x)={{:((|x-1|)/(x-1),"when "xne1),(0,"when "x=1):}

The definition of the function f (x) is given below: f(x)={{:((1)/(2)-x,"when "xlt3 ),(1,"when " x=3),(x-(1)/(2),"when " xgt3):} Calculate f (3-0), f(3+0),f(3) and state whether f (x) is continuous at x =3 or not.

A function f (x) is defined as followes: f(x)={{:(xsin.(1)/(x),"when " xne0),(0,"when " x=0):} Show that f (x) is continuous at x =0 .

Show that the function f(x)={{:(x"cos"(1)/(x),"when"xne0),(0,"when"x=0):} is continuous at x=0.

If the function f(x) ={{:((sinx)/(kx)+k",when "xne0),(2" when "x=0):} is continuous at x = 0, find k.

Define the continuity of a function at a point within its domain of definition. The definition of a function is given below: f(x)={{:((1-cos5x)/(x^(2))," when "(xne0)),(k," when x = 0"):} Find the value of k for which f(x) is continuous at x = 0.

If the following function f (x) is continuous at x = 0 , find k : f(x)={{:((1-cos2mx)/(2x^(2)),"when " xne0),(" " k,"when " x =0):}

Discuss the continuity of the function f, where f is defined by f(x)={{:(2x," if "x lt 0),(0," if "0 le x le 1),(4x," if "x gt 1):} .

CHHAYA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -EXERCISE 2A ( Long Answer Type Questions)
  1. Let f(x)={{:(" "x^(2)/(2),"when " 0lexlt1),(2x^(2)-3x+(3)/(2),"wh...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. A function f (x) is defined as follows : f(x)={{:(3x+1,"for "xle1 ),(...

    Text Solution

    |

  5. A function f (x) is defined as f(x)={{:(ax+2,"when "xle3),(bx+3,"whe...

    Text Solution

    |

  6. Let f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2)),"when " xne2),(" "k,...

    Text Solution

    |

  7. Let f(x)={{:((1-cos2ax)/(xsin2x),"when " xne0),(" " (1)/(2),"when " ...

    Text Solution

    |

  8. If the following function f (x) is continuous at x = 0 , find k : ...

    Text Solution

    |

  9. The function f(x)=(x^(3)-1)/(x-1) is undefined at x = 1 . Redefine the...

    Text Solution

    |

  10. Show that the function f(x)={{:(x+(x+2)/(|x+2|),"when " xne-2),(" "-...

    Text Solution

    |

  11. If the function f(x)={{:(3ax+b,"for "xgt1),(" " 11,"when " x=1),(5...

    Text Solution

    |

  12. Let f(x)={{:((1-sin^(3)x)/(3cos^(2)x),"if "x lt(pi)/(2)),(a,"if "x=(pi...

    Text Solution

    |

  13. Let f(x)={{:((sin(a+1)x+sinx)/(x)",","when " xlt0),(" c,","wh...

    Text Solution

    |

  14. Show that the function f(x)=|sinx+cosx| is continuous at x = pi.

    Text Solution

    |

  15. Show that the function g(x)=x-[x] is discontinuous at all integral po...

    Text Solution

    |

  16. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  17. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  18. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  19. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |

  20. Find from the first principle , the derivatives of the following funct...

    Text Solution

    |