Home
Class 12
MATHS
For x in R, lim(x rarr oo) ((x-3)/(x+2))...

For `x in R, lim_(x rarr oo) ((x-3)/(x+2))^(x)` is equal to :

A

1/e

B

`1/e^(2)`

C

2/e

D

e

Text Solution

Verified by Experts

The correct Answer is:
B
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 oo)((x)/(1+x))^(x) =

lim_(x rarr oo) ((x+6)/(x+1))^(x+4) =

lim_(x rarr oo) ((x+a)/(x+b))^(x+b) =

lim_(x rarr oo) (1-4/(x-1))^(3x-1) =

lim_(x rarr oo) (e^(x^(2)) - cos x)/(x^(2)) is equal to :

lim_(x to oo) ((x-3)/(x+2)) is equal to :

lim_(x rarr oo) (1-2/x)^(x) =

lim_(x to oo) ((x + 6)/(x + 1))^(x + 4) , is equal to

lim_(x rarr 0) (sin x)/(x (1 + cos x)) is equal to :

lim_(x rarr oo)(1+4/(x-1))^(x+3) =

HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. The value of the constant alpha and beta such that lim(x rarr oo) ((x^...

    Text Solution

    |

  2. lim(theta rarr 0) (4 theta(tan theta-sin theta))/(1-cos 2 theta)^2 is

    Text Solution

    |

  3. For x in R, lim(x rarr oo) ((x-3)/(x+2))^(x) is equal to :

    Text Solution

    |

  4. lim(x rarr 0) (cos (sinx )-1)/x^(2) =

    Text Solution

    |

  5. lim(x rarr -2) (sin^(-1)(x+2))/(x^(2)+2x) =

    Text Solution

    |

  6. lim(n rarr oo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1) ) =

    Text Solution

    |

  7. The value of lim(x rarr 0) (sqrt((1)/(2) (1-cos 2x)))/(x) is :

    Text Solution

    |

  8. The value of lim(x rarr 0) (int(0)^(x^(2))cos t^(2)dt)/(x sin x) is :

    Text Solution

    |

  9. lim(x rarr 0) (sin nx[(a-n)nx - tan x])/(x^(2)) = 0, where n is non-ze...

    Text Solution

    |

  10. Let f(2)=4 and f'(2)=4. Then lim(xto2)(xf(2)-2f(x))/(x-2) is given b...

    Text Solution

    |

  11. lim(x rarr oo) (logx^(n)-[x])/([x]), where n in N and [.] denotes the ...

    Text Solution

    |

  12. Let f(a) = g(a) = k and their n^(th) order derivatives exist and are n...

    Text Solution

    |

  13. Let f:R to R be a positive increasing function with lim(x to oo) (f(3x...

    Text Solution

    |

  14. lim(x rarr 0) x^(2). sin (pi/x) is

    Text Solution

    |

  15. If 0 lt x lt y, then lim(n rarroo)(y^(n)+x^(n))^(1/n) is equal to

    Text Solution

    |

  16. The value of lim(x rarr 0) (e^(x)-e^(sinx))/(2 (x-sinx))=

    Text Solution

    |

  17. If f(x) = {((sin(1+[x]))/([x]), for [x] ne 0),(0, for [x] = 0):} , wh...

    Text Solution

    |

  18. If f : R rarr R is defined by f(x) = [x-3]+|x-4| for x in R, then lim(...

    Text Solution

    |

  19. lim(x rarr 0) ((1-e^(x))sin x)/(x^(2)+x^(3)) =

    Text Solution

    |

  20. lim(x rarr 0) (sqrt(1+x)-1)/x =

    Text Solution

    |