Home
Class 12
MATHS
Evaluate: ("lim")(xvec0)(2^x-1)/(sqrt(1+...

Evaluate: `("lim")_(xvec0)(2^x-1)/(sqrt(1+x)-1)`

A

2

B

`log_(e)2`

C

`(log_(e)2)/2`

D

`2 log_(e)2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section - C ( More than one options are correct )|5 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Section - D|6 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Assignment ( section -A)|61 Videos
  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos
  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

Evaluate: ("lim")_(xvec0)(x2^x-x)/(1-cosx)

Evaluate lim_(xto0) (2^(x)-1)/(sqrt(1+x)-1).

Evaluate: ("lim")_(xvec0)(e^x^2-cosx)/(x^2)

Evaluate: ("lim")_(xvec0)(cos^(-1)((1-x^2)/(1+x^2)))/(sin^(-1)x)

Evaluate: ("lim")_(xvec0)((1-3^x-4^x+12^x))/(sqrt((2cosx+7))-3)

Evaluate: ("lim")_(xvec0)(e^x+e^(-x)-2)/(x^2)

Evaluate: ("lim")_(xvec0)(cot2x-cos e c2x)/x

lim_(x to 0) (2^(x) - 1)/(sqrt(1 + x) - 1) =

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)

Evaluate: ("lim")_(xvec-2^+) (x^2-1)/(2x+4)

AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Section -B
  1. Let f(2)=4 and f'(2)=4. Then lim(x->2)(xf(2)-2f(x))/(x-2) is equal to

    Text Solution

    |

  2. If f(4)= 4, f'(4) =1 then lim(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is ...

    Text Solution

    |

  3. Evaluate: ("lim")(xvec0)(2^x-1)/(sqrt(1+x)-1)

    Text Solution

    |

  4. Let alpha and beta be the distinct roots of ax^(2) + bx + c = 0. Then ...

    Text Solution

    |

  5. ("lim")(xvec0)(sin(picos^2x)/(x^2)i se q u a lto -pi (b) pi (c) pi/...

    Text Solution

    |

  6. lim(x->oo)(sqrt(x+sqrt(x))-sqrt(x))equals

    Text Solution

    |

  7. lim(x->0)(1/(x^2)-1/(tan^2x))

    Text Solution

    |

  8. lim(x to oo) ((x-3)/(x+2))^x is equal to :

    Text Solution

    |

  9. underset(xto0)lim((1+tanx)/(1+sinx))^(cosecx) is equal to

    Text Solution

    |

  10. lim(x->0)((4^x+9^x)/2)^(1/x)

    Text Solution

    |

  11. If underset (xrarr0)"lim"(cosx+asinbx)^(1/x)=e^(2) then the possible v...

    Text Solution

    |

  12. underset(x to 0)(Lt) (sqrt(1 - cos 2 x))/(sqrt(2)x) =

    Text Solution

    |

  13. lim(x to 2^+) (([x]^(3))/(3) - [(x)/(3)]^(3)) is where [x] represents ...

    Text Solution

    |

  14. The value of lim(x to 0) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x^...

    Text Solution

    |

  15. If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is co...

    Text Solution

    |

  16. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

    Text Solution

    |

  17. The number of points at which the function f(x) = 1/ (log |2x|) is di...

    Text Solution

    |

  18. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

    Text Solution

    |

  19. The set of points where f(x)=x/(1+|x|) is differentiable is

    Text Solution

    |

  20. The function |x^2 - 3x+2| + cos |x| is not differentiableat x=

    Text Solution

    |