Home
Class 12
MATHS
Examine the continuity of f(x) = {{:((x)...

Examine the continuity of `f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",", "if "x = 0):}` at `x = 0`

Text Solution

Verified by Experts

The correct Answer is:
Discontinuous
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION III)(SHORT ANSWER TYPE QUESTIONS) |3 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION IV)(SHORT ANSWER TYPE QUESTIONS) |14 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION I)(MULTIPLE CHOICE QUESTIONS) |8 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

Examine the continuity of the function: f(x) = {:((x-4)/(2(x-4)), if x ne4),(0, if x =4):} at x =4

Determine the value of k so that following functions are continuous at x = 0 f(x) = {{:((sin 2x)/(x)"," ,"if " x != 0),(k",","if " x = 0):}

Discuss the continuity of the function defined by f(x) = {{:((sin 3x)/(x)"," ,x != 0),(t",", x = 0):} at x = 0

Test the continuity of the following functions at indicated points : f(x) = {{:((x) "sin" 1/(x)"," ,x != 0),(0",", x = 0):} at x = 0

Examine the following functions for continuity: f(x) = {:{((|x-3|)/(2(x-3)), if x ne 3),(0, if x =3):} at x = 3

Examine for continuity the following functions: f(x) = {:(x , if x ne 0),(1 , if x = 0):}

Show that the function f(x) = {{:(2 + x"," , "if " x ge 0),(1",", "if " x lt 0):} is not continuous at x = 0

Test the continuity of the following functions at indicated points : f(x) = {{:(x^2 "sin" 1/x"," ,x != 0),(0",", x = 0):} at x = 0

Examine for continuity the following functions: f(x) = {:(x/|x|, x ne 0),(0, x = 0):}

BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE)(SECTION II)(SHORT ANSWER TYPE QUESTIONS)
  1. Test the continuity of the function at x = 3, where f(x) = {{:((|x-3...

    Text Solution

    |

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

    Text Solution

    |

  3. Examine the continuity of f(x) = {{:((x)/(|x| )"," ,"if " x != 0),(0",...

    Text Solution

    |

  4. If f(x) = {{:((x)/(|x| + 2x^2)"," ,x != 0),(k",", x = 0):} Prove tha...

    Text Solution

    |

  5. Discuss the continuity of the function defined by f(x) = {{:((sin 3x...

    Text Solution

    |

  6. Discuss the continuity of the function defined by f(x) = {{:((tan 2x...

    Text Solution

    |

  7. Test the continuity of the following functions at indicated points : ...

    Text Solution

    |

  8. Test the continuity of the following functions at indicated points : ...

    Text Solution

    |

  9. Test the continuity of the following functions at indicated points : ...

    Text Solution

    |

  10. Determine k, so that f(x) = {{:((x^2 - 36)/(x - 6)"," ,"if " x != 6),(...

    Text Solution

    |

  11. Find k, so that f(x) = {{:((sin kx)/(x)"," ,x != 0),(4+ x",", x = 0):}...

    Text Solution

    |

  12. Determine k, if the following function is continuous at x = 0 f(x) =...

    Text Solution

    |

  13. For what value of k is the function defined by f(x) = {{:(k(x^2 + 2)...

    Text Solution

    |

  14. Find the value of k so that f(x) is continous at x = 0 f(x) = {{:((1...

    Text Solution

    |

  15. Find the value of k so that f(x) is continouns at x = 0 f(x) = {{:((...

    Text Solution

    |

  16. Determine the constant k so that the function f(x) = {{:(3k - 2x"," ...

    Text Solution

    |

  17. Determine the constant lambda , so that the function is continuous at ...

    Text Solution

    |

  18. For what value of k is the following function continous at x = 2 ? f...

    Text Solution

    |

  19. Find all the points of discontinuity, where f is defined by f(x) = {...

    Text Solution

    |

  20. Find all the points of discontinuity, where f is defined by f(x) = {...

    Text Solution

    |