Home
Class 12
MATHS
The value of lim(x->0) [sinx/x] is (wher...

The value of `lim_(x->0) [sinx/x]` is (where `[.]` denotes greatest integer function)

A

1

B

0

C

-1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
` xgt sin x " for all " x gt 0 and x lt sin x " for all " x lt 0`
` rArr (sin x) /(x) lt "for all " x ne 0 rArr lim_(xto0) [(sinx)/(x)]=0`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|101 Videos

  • LIMITS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATHEMATICAL INDUCTION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|30 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(xto0)(sin[x])/([x]) (where [.] denotes the greatest integer function) is

The value of lim_(x->0) [x^2/(sin x tan x)] (Wherer [*] denotes greatest integer function) is

Solve lim_(xto0)["sin"(|x|)/x] , where e[.] denotes greatest integer function.

lim_(xto0)[(-2x)/(tanx)] , where [.] denotes greatest integer function is

The value of int_0^100 [tan^-1 x]dx is, (where [*] denotes greatest integer function)

the value of int_(0)^([x]) dx (where , [.] denotes the greatest integer function)

The value of the lim_(x->0)x/a[b/x](a!=0)(where [*] denotes the greatest integer function) is

Solve (i) lim_(xto1) sin x (ii) lim_(xto0^(+))[(sinx)/x] (iii) lim_(xto0^(-))[(sinx)/x] (where [.] denotes greatest integer function)

lim_(xrarr0) x^8[(1)/(x^3)] , where [.] ,denotes the greatest integer function is

The value of int_(0)^(2)[x+[x+[x]]] dx (where, [.] denotes the greatest integer function )is equal to

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. The value of lim(x->0) [sinx/x] is (where [.] denotes greatest integer...

    Text Solution

    |

  2. Let f(x)={(x^(2),x epsilonZ),((d(x^(2)-4))/(2-x),x !inZ):} the set of ...

    Text Solution

    |

  3. If Sn=sum(k=1)^n ak and lim(n->oo)an=a , then lim(n->oo)(S(n+1)-Sn)/sq...

    Text Solution

    |

  4. If a1=1a n da(n+1)=(4+3an)/(3+2an),ngeq1,a n dif("lim")(nvecoo)an=a , ...

    Text Solution

    |

  5. If x(1)=3 and x(n+1)=sqrt(2+x(n))" ",nge1, then underset(ntooo)limx(n)...

    Text Solution

    |

  6. The value of underset(xrarr0)(lim)(sqrt(1-cosx^(2)))/(1-cos x) is

    Text Solution

    |

  7. Evaluate underset(ntooo)limncos((pi)/(4n))sin((pi)/(4n)).

    Text Solution

    |

  8. Evaluate ("lim")(n→oo){cos(x/2)cos(x/4)cos(x/8)... cos(x/(2^n))}

    Text Solution

    |

  9. If f(x) is the integral of (2 sin x - sin 2x )/(x ^ 3 ) , w...

    Text Solution

    |

  10. Evaluate: ("lim")(xvec0)x^m(logx)^n ,m , n in Ndot

    Text Solution

    |

  11. The value of lim(xrarroo) (logx)/(x^n), n gt 0, is

    Text Solution

    |

  12. underset(xtoa)lim(log(x-a))/(log(e^(x)-e^(a)))

    Text Solution

    |

  13. Let < an > be a sequence such that lim(x->oo)an=0. Then lim(n->oo)(a1...

    Text Solution

    |

  14. If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of ("l...

    Text Solution

    |

  15. If f(9)=9,f^(prime)(9)=4,t h e n("lim")(nvecoo)(sqrt(f(x)-3))/(sqrt(x-...

    Text Solution

    |

  16. A(i)=(x-a(i))/(|x-a(i)|),i=1,2,...,n," and "a(1)lta(2)lta(3)lt...lta(n...

    Text Solution

    |

  17. lim(x -> oo) x^n / e^x = 0, (n is an integer) for

    Text Solution

    |

  18. lim(xrarr0) (x)/(tan^-1x) is equal to

    Text Solution

    |

  19. If f(x) =x , x<0 and f(x)=1 , x = 0, and f(x)=x^2,x>0 then lim(x->0) ...

    Text Solution

    |

  20. Evaluate the following limits : Lim(x to oo) sqrt(((x+sin x)/(x- cos...

    Text Solution

    |

  21. Evaluate: ("lim")(xvecoo)(1+1/(a+b x))^(c+dx),w h e r ea , b , c ,a n ...

    Text Solution

    |