Home
Class 12
MATHS
lim(nrarroo) (1-x+x.root n e)^(n) is eq...

`lim_(nrarroo) (1-x+x.root n e)^(n)` is equal to

A

`e^(x)`

B

`e^(-x)`

C

`e^(2x)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(nrarroo)(lim)(1-x+x.rootn(e))^(n)" "(1^(oo)"form")`
`=e^(underset(nrarroo)(lim)(1-x+xe^(1//n)-1))`
`=e^(x)e^(underset(nrarroo)(lim)((e^(1//n)-1))/(1//n))`
`=e^(x)`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise Multiple Correct Answers Type|4 Videos

  • LIMITS

    CENGAGE|Exercise ComprehensionType|2 Videos

  • LIMITS

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • JEE 2019

    CENGAGE|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

If f:R rarr R is continous function satisying f(0) =1 and f(2x) -f(x) =x, AAx in R , then lim_(nrarroo) (f(x)-f((x)/(2^(n)))) is equal to

lim_(ntooo)((root(3)(n!))/n) is equal to

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

lim_(x rarr oo x rarr equal to e^(n) then n is equal to )(1+(1)/(x(x+4)))^(-x^(2))

lim_(nrarroo) sum_(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

If Sigma_(r=1)^(n)t_(r)=(1)/(6)n(n+1)(n+2), AA n ge 1, then the value of lim_(nrarroo)Sigma_(r=1)^(n)(1)/(t_(r)) is equal to

lim_(x rarr oo)(1-x+x*e^((1)/(n)))^(n)

lim_(xrarr0)((1+x)^(n)-1)/(x) is equal to

CENGAGE-LIMITS-Single Correct Answer Type
  1. If agt0, b gt0 than lim(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

    Text Solution

    |

  2. If f(x)=lim(nrarroo) (cos(x)/(sqrtn))^(n), then the value of lim(xrarr...

    Text Solution

    |

  3. lim(xrarr0) (log(x^(x^(2))+2sqrtx))/(tansqrtx) is equal to

    Text Solution

    |

  4. Let f:RrarrR be such that f(a)=1, f(a)=2. Then lim(x to 0)((f^(2)(a+x)...

    Text Solution

    |

  5. The value of lim(nrarroo) ((sqrtn^(2)+n-1)/(n))^(2sqrt(n^(2)+n-1)) is

    Text Solution

    |

  6. If f(n)=lim(xrarr0) ((1+sin.(x))/(2))(1+sin.(x)/(2^(2)))...(1+sin.(x)/...

    Text Solution

    |

  7. lim(nrarroo) (1-x+x.root n e)^(n) is equal to

    Text Solution

    |

  8. The value of lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

    Text Solution

    |

  9. lim(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

    Text Solution

    |

  10. The value of lim(x rarr 0) (1-cos2x)/(e^(x^(2))-e^(x)+x) is

    Text Solution

    |

  11. If f(a)=(1)/(4), then lim(hrarr0) (f(a+2h^(2))-f(a-2h^(2)))/(f(a+h^(3)...

    Text Solution

    |

  12. lim(xrarr0^(+)) (1)/(xsqrtx)(a tan^(-1).(sqrtx)/(a)-btan^(-1).(sqrtx)/...

    Text Solution

    |

  13. The value of lim(xrarr0) ((1+2x)/(1+3x))^((1)/(x^(2))).e^((1)/(e^(x)))...

    Text Solution

    |

  14. If F:R rarr R be a differentiable function at x = 0 satisfying f(0)=0 ...

    Text Solution

    |

  15. The value of lim(xrarr(3pi)/(4)) (1+root3(tanx))/(1-2cos^(2)x) is

    Text Solution

    |

  16. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

    Text Solution

    |

  17. Number of integral values of lambda for which lim(xrarr1) sec^(-1)((la...

    Text Solution

    |

  18. If lim(xrarr0) (e^(ax)-e^(x)-x)/(x^(2))=b (finite), then

    Text Solution

    |

  19. If lim(xrarr0)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is equal to

    Text Solution

    |

  20. If lim(xrarroo) xlog(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,0,1//x)|)...

    Text Solution

    |