Home
Class 11
MATHS
Evaluate the following limits using sand...

Evaluate the following limits using sandwich theorem: `lim_(x->oo)([x])/x ,w h e r e[dot]` represents greatest integer function.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • LINEAR INEQUALITIES

    CENGAGE ENGLISH|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following limits using sandwich theorem: ("lim")_(xvecoo)((log)_e x)/x

Evaluate: ("lim")_(xvec0)(sinx)/x,w h e r e[dot] represents the greatest integer function.

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

Evaluate: int_0^(100)(x-[x]dx(w h e r e[dot] represents the greatest integer function).

Evaluate: ("lim")_(xvec0)(tanx)/x where [dot] represents the greatest integer function

Evaluate: [("lim")_(xto0)(tanx)/x] where [dot] represents the greatest integer function

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

Find the range of f(x)=(x-[x])/(1-[x]+x '),w h e r e[] represents the greatest integer function.

Evaluate: int_0^(100)x-[x]dx where [dot] represents the greatest integer function).

CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate the following limits using sandwich theorem: ("lim")(xvecoo)(...

    Text Solution

    |

  2. The value of lim(x rarr 1)(2-x)^(tan((pix)/2)) is (a) e^(-2/pi) (b) e...

    Text Solution

    |

  3. Evaluate the following limits using sandwich theorem: lim(x->oo)([x])...

    Text Solution

    |

  4. lim(x->0)(sinx)^n/(sinx)^m,(mltn), is equal to (a)1 (b) 0 (c) n//m ...

    Text Solution

    |

  5. If (x^2+x−2)/(x+3) <= (f(x))/x^2 <= (x^2+2x−1)/(x+3) hold for a certai...

    Text Solution

    |

  6. lim(x->oo)(2sqrt(x)+3root3x+4root4x+.......+nrootnx)/(sqrt((2x-3))+roo...

    Text Solution

    |

  7. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2ltf(x)lt(x^2|...

    Text Solution

    |

  8. ("lim")(xvec0)((x+y)sec(x+y)-xsecx)/yi se q u a lto secx(xtanx+1) (b...

    Text Solution

    |

  9. Evaluate : ("lim")(xrarroo) 1/(1+n^2)+2/(2+n^2)+...+n/(n+n^2)

    Text Solution

    |

  10. If L=lim(x-&gt;2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| ...

    Text Solution

    |

  11. Suppose that f is a function such that 2x^2lt=f(x)lt=x(x^2+1) for all ...

    Text Solution

    |

  12. If L=lim(x->0)(e^(-(x^2/2))-cosx)/(x^3 sinx), then the value of 1/(3L)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the val...

    Text Solution

    |

  16. If f(x)={x-1,xgeq 1 2x^2-2,x<1,g(x)={x+1,x >0-x^2+1,xlt=0,a n dh(x) ...

    Text Solution

    |

  17. Evaluate the limits using the expansion formula of functions ("lim")(x...

    Text Solution

    |

  18. lim(xrarrinfty),where (2x-3)/xltf(x)lt(2x^2+5x)/x^2,is

    Text Solution

    |

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

    Text Solution

    |

  20. If lim(x->0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(lim(x-...

    Text Solution

    |