Home
Class 12
MATHS
Show that f(x)={(x-|x|)/2,\ \ \ w h e n\...

Show that `f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 2,\ \ \ w h e n\ x=0` is discontinuous at `x=0` .

Text Solution

AI Generated Solution

To show that the function \[ f(x) = \begin{cases} \frac{x - |x|}{2} & \text{when } x \neq 0 \\ 2 & \text{when } x = 0 \end{cases} ...
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

  • DEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|567 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(sin3x)/x,w h e nx!=0 1,w h e nx=0dot Find whether f(x) is continuous at x=0

Show that f(x)={(x-|x|)/(2),2 w h e nx!=0i sd i s con t inuou sa tx=0dotw h e nx=0

Show that the function f(x) given by f(x)={(e^(1/x)-1)/(e^(1/x)+1), when x!=00,quad when x=0 is discontinuous at 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)=(e^((1)/(x))-1)/(1+e^((1)/(x))) when x!=0=0, when x=0 show that f(x) is discontinuous at x=0

Let f(x)={x^(n),x is rational and -x^(n),x is irrational then f(x) is discontinuous at x=0 if n

Find the value of a for which the following function is continuous at a given point. f(x)={(x^2+3x-10)/(x^2+2x-15),\ w h e n\ x!=-5a ,\ w h e n\ x=-5

f(x)=[(sinx)/x ,"w h e n"x!=0=2,"w h e n"x=0 sinx-, when x0/(x) =L= 2, when x=0

Find the derivative of f(x)={(x-1)/(2x^2-7x+5)w h e nx!=1=1/3w h e nx=1a tx=1.

1.If lim_(x rarr0)(f(x))/(x) exists and f(0)=0 then f(x) is (a) continuous at x=0 (b) discontinuous at x=0 (e) continuous no where (d) None of these

RD SHARMA-CONTINUITY-Solved Examples And Exercises
  1. If f(x)={e^(1//x),\ \ \ if\ x!=0 1,\ \ \ if\ x=0 . Find whether f is c...

    Text Solution

    |

  2. Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 1,\ \ \ \ w h e n\ x=0 . ...

    Text Solution

    |

  3. Show that f(x)={(x-|x|)/2,\ \ \ w h e n\ x!=0 2,\ \ \ w h e n\ x=0 is ...

    Text Solution

    |

  4. Show that f(x)={(|x-a|)/(x-a),\ \ \ w h e n\ x!=a1,\ \ \ w h e n\ x=a ...

    Text Solution

    |

  5. Discuss the continuity of f(x)={|x|cos(1/x),\ \ \ x!=0 0,\ \ \ \ x=...

    Text Solution

    |

  6. Discuss the continuity of f(x)={x^2sin(1/x),\ \ \ \ x!=0\ \ \ \ \ \...

    Text Solution

    |

  7. Discuss the continuity of f(x)={(x-a)sin(1/(x-a)),\ \ \ x!=a\ \ \ \...

    Text Solution

    |

  8. f(x)={(e^x-1)/(log(1+2x)),\ \ \ if\ x!=0\ \ \ \ \ \ \ \ \ 7,\ \ \ \ \ ...

    Text Solution

    |

  9. f(x)={(1-x^n)/(1-x),\ \ \ x!=1 ,\ \ \ n-1,\ \ \ x=1\ \ \ \ n in N a...

    Text Solution

    |

  10. f(x)={(|x^2-1|)/(x-1),\ \ \ for\ x!=1 2,\ \ \ for\ x=1 at x=1

    Text Solution

    |

  11. f(x)={(2|x|+x^2)/x ,\ \ \ x!=0 ,\ \ \ and 0 at x=0 is continuous at ...

    Text Solution

    |

  12. f(x)={|x-a|sin(1/(x-a)),\ \ \ for\ x!=a0,\ \ \ for\ x=a at x=a

    Text Solution

    |

  13. Show that f(x)={1+x^2,\ \ \ if\ 0lt=xlt=1 2-x ,\ \ \ if\ x >1 is disco...

    Text Solution

    |

  14. Show that f(x)={(sin3x)/(tan2x),\ \ \ if\ x<0 3/2,\ \ \ if\ x=0(log(1+...

    Text Solution

    |

  15. Find the value of ' a^(prime) for which the function f defined by f(x)...

    Text Solution

    |

  16. Examine the continuity of the function f(x)={3x-2,\ \ \ xlt=0x+1,\ ...

    Text Solution

    |

  17. Discuss the continuity of the function f(x)={x ,\ \ \ x >0 1,\ \ \ ...

    Text Solution

    |

  18. Discuss the continuity of the function f(x)={(x , 0 le x lt1/2 12),...

    Text Solution

    |

  19. Discuss the continuity of f(x)={2x-1,\ \ \ x<0 2x+1,\ \ \ xgeq0 at ...

    Text Solution

    |

  20. For what value of k is the function f(x)={(x^2-1)/(x-1),\ \ \ x!=1k ,\...

    Text Solution

    |