Home
Class 11
MATHS
Find the left hand and right hand limits...

Find the left hand and right hand limits of greatest integer function f(x) = [x] = greatest integer less than or equal to x, at x = k, where k is an integer.

Promotional Banner

Topper's Solved these Questions

  • INTRODUCTIONS TO 3-D COORDINATE GEOMETRY

    RD SHARMA|Exercise Solved Examples And Exercises|114 Videos

  • LINEAR INEQUATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|163 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=x-[x]+cos x, where [x]= the greatest integer less than or equal to x is a

Let f(x)=[x^(2)+1],([x] is the greatest integer less than or equal to x) . Ther

If f(x)=|x-1|-[x] (where [x] is greatest integer less than or equal to x ) then.

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

The solutions of the equation 2x-2[x]=1, where [x]= the greatest integer less than or equal to x, are

Let [x] denotes the greatest integer less than or equal to x and f(x)= [tan^(2)x] .Then

Find all the points of discontinuity of the greatest integer function defined by f(x)=[x], where [x] denotes the greatest integer less than or equal to x.

RD SHARMA-LIMITS-All Questions
  1. Suppose f(x)={(a+bx, x<1), (4, x=1), (b-ax, x>1):} and if lim(xto1) f(...

    Text Solution

    |

  2. Find the left hand and right hand limits of greatest integer function ...

    Text Solution

    |

  3. Prove that lim(x->a^+) [x]=[a] for all a in R, where [*] denotes the ...

    Text Solution

    |

  4. If f is an even function, then prove that lim(x->0^-) f(x) = lim(x->0^...

    Text Solution

    |

  5. Show that ("lim")(x->0)x/(|x|) does not exist.

    Text Solution

    |

  6. Find k so that ("lim")(x->2)\ f(x) may exist, where f(x)={2x+3,\ xlt=2...

    Text Solution

    |

  7. Show that ("lim")(x->0)1/x does not exist.

    Text Solution

    |

  8. Let f(x)={x+1,\ if\ x >0, x-1,\ if\ x<0dot Prove that ("lim")(x->1)\ f...

    Text Solution

    |

  9. Let f(x)=\ {x+5,\ if\ x >0x-4,\ if\ x<0 Prove that ("lim")(x->0)\ f(x)...

    Text Solution

    |

  10. Find ("lim")(x->3)\ f(x),\ w h e r e\ f(x)={4,\ if\ x >3x+1,\ if\ x<3

    Text Solution

    |

  11. Find lim(xrarr0)f(x)a n d(lim)(x-&gt;1)f(x),""""w h e r e""""f(x)=[2x+...

    Text Solution

    |

  12. Find (lim)(x->1)f(x),""w h e r e""f(x)=[x^2-1, xlt=1-x^2-1, x >1

    Text Solution

    |

  13. Evaluate ("lim")(x->0)f(x),\ w h e r e\ f(x)={(|x|)/x ,\ x!=0 0,\ x=0

    Text Solution

    |

  14. Find ("lim")(x->1^+)1/(x-1)dot

    Text Solution

    |

  15. Evaluate the following one sided limit: ("lim")(x->2^-)\ (x-3)/(x^2-4)

    Text Solution

    |

  16. Evaluate the following one sided limit: lim(x->-8^+)(2x)/(x+8)

    Text Solution

    |

  17. Evaluate the following one sided limit: ("lim")(x->pi//2^+)secx

    Text Solution

    |

  18. Evaluate the following one sided limit: ("lim")(x->-pi//2^+)(2-cotx)

    Text Solution

    |

  19. Evaluate the following one sided limit: ("lim")(x->2^-)\ (x-3)/(x^2-4)

    Text Solution

    |

  20. Evaluate the following one sided limit: ("lim")(x->0^+)2/(x^(1//5))

    Text Solution

    |