Home
Class 12
MATHS
Lt(xto0)(sqrt(1+x)-1)/(x) is equal to ...

`Lt_(xto0)(sqrt(1+x)-1)/(x)` is equal to
(i) 0
(ii) 1
(iii) `1/2`
(iv) 2

A

`1//2`

B

2

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
` lim_(x to 0) (sqrt(1+x-1))/(x) =lim_(xto0)(x)/(x{sqrt(1+x+1)})=lim_(xto 0) (1)/(sqrt(1+x)+1)=(1)/(2)`
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

Lt_(xto0)(sqrt(4+x)-2)/(sinx) is equal to (i) 4 (ii) 1 (iii) 1/4 (iv) 0

Lt_(x to 0)(e^(x)+sinx-1)/(3x) is equal to (i) 1/3 (ii) -1/3 (iii) 2/3 (iv) -2/3

Lt_(xto0)(x)/(sin3x) is equal to (i) 3 (ii) 1/3 (iii) 0 (iv) 1

Lt_(x to 0)(a^(x)-1)/(sqrt(1+x)-1) is equal to

Lt_(xto0)(x^(2)cosx)/(1-cosx) is equal to

Lt_(x to 0)(|x|)/(x) is equal to (i) 1 (ii) -1 (iii) 0 (iv) does not exist

Lt_(xto0)(|sinx|)/(x) is equal to (i) 1 (ii) -1 (iii) does not exist (iv) none of these

lim_(xto0) (sqrt(1-cos 2x))/(sqrt2x) is equal to-

Lt_(xto1)(sinpix)/(x-1) is equal to

Lt_(x to (pi)/(2))(pi/2-x)tan x is equal to (i) 1 (ii) -1 (iii) (pi)/(2) (iv) (2)/(pi)

OBJECTIVE RD SHARMA ENGLISH-LIMITS-Chapter Test
  1. Lt(xto0)(sqrt(1+x)-1)/(x) is equal to (i) 0 (ii) 1 (iii) 1/2 ...

    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

    |