Home
Class 11
MATHS
If [dot] denotes the greatest integer fu...

If `[dot]` denotes the greatest integer function, then find the value of `lim_(x->0)` `([x]+[2x]++[n x])/(n^2)`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If f(x) =cos [pi^(2)]x+ cos [-pi^(2)] x, where [x] denots the greatest integer function, then the value of f((pi)/(2)) is-

If [x+[2x]] lt3 , where [.] denotes the greatest integer function, then x is

[x] denote the greatest integer function. The value of int_(1)^(a)[x]f^(')(x)dx,agt1 is-

If [.] denotes the greatest integer function then lim_(x→0) ​ [x^2/(tanx.sinx)] =

If [x] denotes the greatest integer lex and n inN then value of I_n=int_0^(n^2) [sqrtx]dx is

Let f(x)={1+|x|,x<-1 [x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2.3)}dot

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :

I=int_0^2x[2x]dx where [.] denotes the greatest integer function then the value of 16/17I must be

If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the greatest integer function, is continuous in [4,6], then find the values of adot

If [x]^2-5[x]+6=0 (where [.] denotes the greatest integer function), then x belongs to

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Suppose that f is a function such that 2x^2lt=f(x)lt=x(x^2+1) for all ...

    Text Solution

    |

  2. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then find the value o...

    Text Solution

    |

  3. If [dot] denotes the greatest integer function, then find the value of...

    Text Solution

    |

  4. If lim(x->oo) f(x) exists and is finite and nonzero and if lim(x->oo)...

    Text Solution

    |

  5. If 3-((x^(2))/(12))lef(x)le3+((x^(3))/(9)) in the neighborhood of x=0,...

    Text Solution

    |

  6. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xg...

    Text Solution

    |

  7. Evaluate underset(xto0)lim{(sinx-x+(x^(3))/(6))/(x^(5))}.

    Text Solution

    |

  8. underset(xtooo)limf(x)," where "(2x-3)/(x)ltf(x)lt(2x^(2)+5x)/(x^(2))A...

    Text Solution

    |

  9. Evaluate underset(xto0)lim(sinx+log(1-x))/(x^(2)).

    Text Solution

    |

  10. If underset(xto0)lim[1+x+(f(x))/(x)]^(1//x)=e^(3), then the value of l...

    Text Solution

    |

  11. Evaluate the limits using the expansion formula of functions lim(x->0)...

    Text Solution

    |

  12. The value of ("lim")(n->oo)[(n+1)^2 3-(n-1)^2 3] is

    Text Solution

    |

  13. Evaluate : lim(x->2)(x^2-5x+6)/(x^2-4)

    Text Solution

    |

  14. If: ("lim")(xrarr1)(1+a x+b x^2)^(c/((x-1)))=e^3, then Find the condit...

    Text Solution

    |

  15. Evaluate : lim(x->1)(2/(1-x^2)+1/(x-1))

    Text Solution

    |

  16. lim(x->0)((1+5x^2)/(1+3x^2))^(1//x^2)=

    Text Solution

    |

  17. Evaluate : lim(x->1)(x^2+x(log)e x-(log)e x-1)/((x^2-1)

    Text Solution

    |

  18. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

    Text Solution

    |

  19. Evaluate lim(x->pi/4)(1-sin2x)/(1+cos4x)

    Text Solution

    |

  20. The value of underset(xtooo)lim(log(e)(log(e)x))/(e^(sqrt(x))) is .

    Text Solution

    |