Home
Class 12
MATHS
The value of underset( x rarr 0 ) ( "Lim...

The value of `underset( x rarr 0 ) ( "Lim") ( sin ( ln ( 1+ x)))/( ln ( 1+ sin x ))` is

A

`0`

B

`1//2`

C

`1//4`

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    MOTION|Exercise EXERCISE -2( LEVEL-I)|16 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-2(LEVEL-2)|5 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    MOTION|Exercise Exercise -4 Level -II|7 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

Similar Questions

Explore conceptually related problems

Evaluate : underset( x rarr0 ) ("lim") ( sqrt( ( 1+sin 3x))-1)/(ln ( 1+ tan 2x))

Evaluate underset( x rarr0 ) ( "Lim") ( 3 sin x - sin 3x)/( x- sin x )

Find underset( x rarr 0 ) ( "Lim") ( e^(sin x) -sin x -1)/( x^(2))

underset( x rarr 0 ) ( "lim")((1+sin x )/( 1- sin x ))^("cosec x ") is equal to :

For x gt 0, underset( x rarr 0) ( "Lim") [ ( sin x)^(1//x) + ((1)/( x))^("sinx ) ] is

The value of lim_(x rarr1)(log x)/(sin pi x) is

lim_(x rarr0)(ln(sin3x))/(ln(sin x)) is equal to

underset(x to 0)lim x log sin x is equal to

If l = underset( x rarr 0) ("Lim")( x ( 1+ a cos x ) - bsin x ) /( x^(3))= underset( x rarr 0 ) ("Lim") ( 1+a cos x ) /( x^(2))- underset( x rarr 0 ) ("lim")( b sin x )/( x^(3)) , where l in R , then

The value of lim_(x rarr0^(+))(sin x)^(1/ln x) is

MOTION-LIMIT-EXERCISE -1
  1. Evaluate: underset(hrarr0)("lim")(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(...

    Text Solution

    |

  2. lim(x->0) sin(6x^2)/(lncos(2x^2-x)

    Text Solution

    |

  3. The value of underset( x rarr 0 ) ( "Lim") ( sin ( ln ( 1+ x)))/( ln (...

    Text Solution

    |

  4. underset( x rarr pi //2) ("Lim") ( 2 ^(cos x) - 1)/( x ( x-pi //2))= ...

    Text Solution

    |

  5. lim(x->0)((4^x-1)^3)/(sin(x/p)ln(1+(x^2)/3) is equal to

    Text Solution

    |

  6. The limit underset( x rarr a ) ("Lim") (2 -( a)/(x))^(tan ((pix)/( 2a)...

    Text Solution

    |

  7. underset( x rarr oo) ( "Lim") ((x+ 2)/( x-2))^(x+1)=

    Text Solution

    |

  8. The value of underset( x rarr pi //4) ("Lim") ( 1+[x])^(1//ln( tan x)...

    Text Solution

    |

  9. lim(x->oo) ((x^2-2x+1)/(x^2-4x+2))^x is equal to

    Text Solution

    |

  10. underset( x rarr 0 ) ("lim") ( cos mx )^(n//x^(2))

    Text Solution

    |

  11. If lim(x -> oo) (1 + a/x + b/x^2)^(2x)= e^2 then the values of a and ...

    Text Solution

    |

  12. underset( x rarr0 ) ( "lim" )( cot ((pi)/( 4) + x ))^("cosecx")=

    Text Solution

    |

  13. lim(x->oo)(sin(1/x)+cos(1/x))^x

    Text Solution

    |

  14. lim(x->oo) (root(3)(1+x)-root(3)(1-x))/x

    Text Solution

    |

  15. underset( x rarr 1 )("lim")( root ( 3)(7+x^(3))- sqrt( 3 +x^(2)))/( x-...

    Text Solution

    |

  16. ABC is an isosceles triangle described in a circle of radius r.If AB=...

    Text Solution

    |

  17. The figure shows a right triangle with its hypotenuse OB along the y-a...

    Text Solution

    |

  18. lim(n->oo){(n/(n+1))^alpha+sin(1/n)}^n where alpha epsilon Q is equal ...

    Text Solution

    |

  19. underset( x rarr 0 ) ( "lim")( x tan 2x - 2x ta n x )/(( 1- cos 2x)^(...

    Text Solution

    |

  20. If underset( x rarr0 )("lim")((sin nx) [ ( a-n ) nx - 2 tan x])/( x^(2...

    Text Solution

    |