Home
Class 12
MATHS
If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x...

If `lim_(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3` , the `a` is equal to

A

2

B

`3/2`

C

`1/2`

D

`2/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Paper|12 Videos
  • LIMITS AND CONTINUITY

    MCGROW HILL PUBLICATION|Exercise Exercise (Numerical Answer)|16 Videos
  • JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )

    MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos
  • MATHEMATICAL INDUCTION AND BINOMIAL THEOREM

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If lim_(xrarr oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

lim_(xto oo)(x/(1+x))^(x) is

If lim_(x rarr oo)(1+(a)/(x)+(b)/(x^(2)))^(3x)=e^(4) then the values of a and b are

If lim_(x rarr oo)((x^(2)+x+1)/(x+1)-ax-b)=4 " then a & b is equal to"

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

lim_(xto oo) (int_(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1)) is equal to

lim_(xrarr oo) ((3x^2+2x+1)/(x^2+x+2))^((6x+1)/(3x+1)) , is equal to

(lim_(xto oo) ((x+3)/(x+1))^(x+1) is equal to

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Questions for Previous Years AIEEE/JEE Main Papers
  1. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

    Text Solution

    |

  2. Let a , b in R,(a in 0). If the funtion f defined as f(x)={{:(,(2x^(...

    Text Solution

    |

  3. Lim( x -> 0) (1 -cos2x)^2 / (2xtanx - x tan2x) is

    Text Solution

    |

  4. Let p=lim(x->0^+)(1+tan^2 sqrt(x))^(1/(2x)) then log p is equal to

    Text Solution

    |

  5. If lim(xto oo) (1+(a)/(x)-(4)/(x^2))^(2x)=e^3 , the a is equal to

    Text Solution

    |

  6. lim(x->3) (sqrt(3x)-3)/(sqrt(2x-4)-sqrt2) is equal to

    Text Solution

    |

  7. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  8. The value of lim(xto pi//2)(cot x-cosx)/(pi-2x)^3 is

    Text Solution

    |

  9. For each t in R let [t] be the greatest integer less than or equal to ...

    Text Solution

    |

  10. lim(x to 0) (x tan 2x -2x tan x)/((1- cos 2x)^(2)) equal

    Text Solution

    |

  11. lim(x-gt0)((27+x)^(1/3)-3)/(9-(27+x)^(2/3))

    Text Solution

    |

  12. If the function f defined as f(x) = 1/x - (k-1)/(e^(2x)-1), x != 0, is...

    Text Solution

    |

  13. lim(y->oo)(sqrt(1+sqrt(1+y^(4)))-sqrt(2))/(y^(4))= (a) (1)/(4sqrt...

    Text Solution

    |

  14. For each x in R, let [x] be the greatest integer less than or equal t...

    Text Solution

    |

  15. For each t in RR, let [t] be the greatest integer less than or equal t...

    Text Solution

    |

  16. Let [x] denote the greatest integer less than or equal to Then: li...

    Text Solution

    |

  17. underset(x to 0) lim(x cot(4x))/(sin^(2) x cot^(2)(2x)) is equal to

    Text Solution

    |

  18. underset(xto pi/4)lim(cot^3x-tanx)/(cos(x+pi/4)) is

    Text Solution

    |

  19. underset(x to 1-)lim (sqrtpi-sqrt(2 sin^(-1) x))/sqrt(1-x) is equal t...

    Text Solution

    |

  20. Let f:Rto R be a function defined as f(x)={{:(5,"if" x le 1),(a+bx , ...

    Text Solution

    |