Home
Class 12
MATHS
The value of lim(xrarroo)[(e^(2))/((1+(2...

The value of `lim_(xrarroo)[(e^(2))/((1+(2)/(x))^(x))]^(x)` is equal to

A

`e^(2)`

B

`e^(-1)`

C

`e^((1)/(2))`

D

`e^(-(1)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • NTA JEE MOCK TEST 65

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos
  • NTA JEE MOCK TEST 67

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(xrarroo)[(e^(2))/((1+(2)/(x))^(x))]^((x)/(2)) is equal to

The value of lim_(xrarroo) x^(2)(1-cos.(1)/(x)) is

lim_(xrarroo) (2x)/(1+4x)

The value of lim_(xrarroo) {(x^2sin((1)/(x))-x)/(1-|x|)} , is

The value of lim_(xrarroo) (sinx)/(x) , is

The value of lim_(xrarr-oo)(x^(2)tan((1)/(x)))/(sqrt(4x^(2)-x+1)) is equal to

The value of lim_(xrarroo) ((x+3)/(x-1))^(x+1) is

The value of lim_(xrarroo) ((x-1)/(x+1))^(x) , is

The value of lim_(xrarroo)((x+6)/(x+1))^(x+4) , is

The value of lim_(x rarr0)((e^(1/x^(2))-1)/(e^(1/x^(2)+1))) is :

NTA MOCK TESTS-NTA JEE MOCK TEST 66-MATHEMATICS
  1. Let x(1), x(2),…..,x(3) be n observations such that Sigmax(i)^(2)=300 ...

    Text Solution

    |

  2. The domain of the function f(x)=(1)/(sqrt([x]^(2)-[x]-20)) is (where, ...

    Text Solution

    |

  3. The value of lim(xrarroo)[(e^(2))/((1+(2)/(x))^(x))]^(x) is equal to

    Text Solution

    |

  4. A person standing at the foot of a tower walks a distance of 3 meters ...

    Text Solution

    |

  5. 12 people are asked questions in succession in a random order and exac...

    Text Solution

    |

  6. Let P(1):x +y+2z-4=0 and P(2): 2x-y+3z+5=0 be the planes. Let A(1, 3, ...

    Text Solution

    |

  7. A point P moves such that the chord of contact of P with respect to th...

    Text Solution

    |

  8. If A and B are square matrices of the same order such that A=-B^(-1)AB...

    Text Solution

    |

  9. The point P(2, 1) is shifted through a distance of 3sqrt2 units measur...

    Text Solution

    |

  10. The value of lambda in R such that (x, y, z) ne (0, 0, ) and (2hati+3h...

    Text Solution

    |

  11. Let there be two prabolas y^(2)=4x and y^(2)=-8x. Then the locus of th...

    Text Solution

    |

  12. If z(1)=2+3i, z(2)=3-2i and z(3)=-1-2sqrt3i, then which of the followi...

    Text Solution

    |

  13. If |(x^(2)+mx+1)/(x^(2)+x+1)|lt3 for all real x, then

    Text Solution

    |

  14. The arithmetic mean of two numbers is 18(3)/(4) and the positive squar...

    Text Solution

    |

  15. The area (in sq. units) bounded by x^(2)+y^(2)=1 and the curve y^(2)ge...

    Text Solution

    |

  16. If 0 lt alpha lt (pi)/(16) and (1+tan alpha)(1+tan4alpha)=2, then the ...

    Text Solution

    |

  17. If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing ...

    Text Solution

    |

  18. If the value of the limit lim(nrarroo)(1^(10)+2^(10)+…n^(10))/(n^(11))...

    Text Solution

    |

  19. The solution of the differential equation ycosx.dx=sinx.dy+xy^(2)dx is...

    Text Solution

    |

  20. 5^2 5^4 5^6...................5^(2x)=(0.04)^-28 ,

    Text Solution

    |