Home
Class 12
MATHS
lim(x rarr 0) (1-ax)^(1/x) =...

`lim_(x rarr 0) (1-ax)^(1/x) =`

A

`e^(-a)`

B

e

C

`e^(a)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|219 Videos

  • LINEAR INEQUALITIES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|54 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr 0) (1+ax)^(b/x)=

If lim_(x rarr 0) (1+px)^(q//x) = e^(4) , where p, q, in N, then :

lim_(x rarr 0) ((1+x)^(n)-1)/x is

If lim_(x rarr 0) (1 + px)^(q/x) = e^(4), where p,q in N , then

For x gt 0, lim_(x rarr 0) ((sin x)^(1//x) + ((1)/(x))^(sin x)) is :

lim_(x rarr 0) (1-cos 4x)/(x2) =

lim_(x rarr 0) (a^(x)-b^(x))/x =

lim_(x rarr 0) ((a^(x) + b^(x) + c^(x))/(3))^(2//x) is equal to :

The value of lim_(x rarr 0) ((e^(x)-1)/x)

lim_(x rarr 0) (sqrt(1+x)-1)/x =

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1...

    Text Solution

    |

  2. If f(a)=2,f'(a)=1,g(a)=-3,g'(a)=-1 then Lim(xtoa)(f(a)g(x)-f(x)g(a))/(...

    Text Solution

    |

  3. lim(x rarr 0) (1-ax)^(1/x) =

    Text Solution

    |

  4. Lim(nto oo)(3^(n)+4^(n))^((1)/(n))=

    Text Solution

    |

  5. lim(x rarr oo) (1-4/(x-1))^(3x-1) =

    Text Solution

    |

  6. The value of lim(x rarr 1) (tan^(2)(x-1))/(x^(3)-x^(2)-x+1) =

    Text Solution

    |

  7. lim(theta rarr pi/2) (pi/2- theta)/(cot theta) =

    Text Solution

    |

  8. lim(x rarr 0) (tan x - sin x)/(x^(3)) =

    Text Solution

    |

  9. The value of lim(x to 0)(5^(x)-5^(-x))/(2x)=

    Text Solution

    |

  10. lim(x-1)(tan(x^(2)-1))/(x-1) is equal to

    Text Solution

    |

  11. The value of lim(x rarr oo) (3^(x+1) - 5^(x+1))/(3^(x)-5^(x) is

    Text Solution

    |

  12. If G(x) = -sqrt(25-x^(2)) the lim(x rarr 1) (G(x)-G(1))/(x-1) =

    Text Solution

    |

  13. lim(n rarr oo) ((1)/(1-n^(2)) + (2)/(1-n^(2)) +…...+(n)/(1-n^(2))) is ...

    Text Solution

    |

  14. lim(x rarr oo) ((2 + x)^(40) (4 + x)^(5))/((2-x)^(45)) is :

    Text Solution

    |

  15. lim(x rarr oo) x^(n)/e^(x) = 0 (n is an integer) for

    Text Solution

    |

  16. If f(x) = sqrt((x-sinx)/(x+cos^(2)x)), then lim(x rarr oo) f(x) =

    Text Solution

    |

  17. lim(x rarr 0) {tan (pi/4+x)}^(1/x) =

    Text Solution

    |

  18. The value of lim(x rarr 0) ((1 + 5x^(2))/(1+3x^(2)))^(1//x^(2)) is :

    Text Solution

    |

  19. lim(x rarr 1) (sqrt(1 - cos 2 (x - 1)))/(x -1) :

    Text Solution

    |

  20. lim(x rarr 0) (sin (pi cos^(2)x))/(x^(2)) is equal to :

    Text Solution

    |