Home
Class 12
MATHS
If L=-lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...

If `L=-lim_(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^(2)+1)))`, then the value of `L^(4)` is _____________.

A

`-(1)/(4)`

B

`(1)/(2)`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
`(6)`
Clearly, n is even. Then,
`underset(ntooo)lim"("2^(1+3+5+...+n//2" terms ").3^(2+4+6+...+n//2" terms")")"^((1)/((n^(2)+1)))`
`=underset(ntooo)lim(2^((n^(2))/(4)).3^((n(n+2))/(4)))^((1)/((n^(2)+1)))`
`=2^(underset(ntooo)lim(1)/(4(1+(1)/(n^(2))))).3^(underset(ntooo)lim((1+(2)/(n)))/(4(1+(1)/(n^(2)))))`
`=2^((1)/(4))3^((1)/(4))=(6)^((1)/(4))`
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE|Exercise JEE Main Previous Year|8 Videos

  • LIMITS

    CENGAGE|Exercise JEE Advanced Previous Year|7 Videos

  • LIMITS

    CENGAGE|Exercise Exercise (Matrix)|5 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

5(2)^((1)/(3))xx3(4)^((1)/(3))xx2(2)^((1)/(3))

If 3^(6)xx9^(2)=3^(n)xx3^(2) , then value of n is

(9^(n)xx3^(2)xx3^(n)-(27)^(n))/((3^(3))^(5)xx2^(3))=(1)/(27)

(3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

if (9^nxx3^2xx3^n-(27)^n)/((3^3)^5xx2^3)=1/(27), find the value of n

Simplify: (((-2)/3)^(-2))^(3)xx(1/3)^(-4)xx3^(-1)xx1/6

1xx3xx5xx7xx9xx...xx(2n-1)=

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

CENGAGE-LIMITS-Exercise (Numerical)
  1. If lim(xtooo) f(x) exists and is finite and nonzero and if lim(xtooo) ...

    Text Solution

    |

  2. If L=lim(xto2)((10-x)^(1//3)-2)/(x-2), then the value of |1//(4L)|" is...

    Text Solution

    |

  3. If lim(xto0) (p sin2x+(1-cos2x))/(x+tanx)=1, then the value of p is.

    Text Solution

    |

  4. The value of lim(xtooo) ((100)/(1-x^(100))-(50)/(1-x^(50))) is .

    Text Solution

    |

  5. If L= lim(xto2) (root(3)(60+x^(2))-4)/(sin(x-2)), then the value of 1/...

    Text Solution

    |

  6. The value of lim(xtooo) ((20^(x)-1)/(19(5^(x))))^(1//x) is .

    Text Solution

    |

  7. The value of lim(ntooo) [root(3)((n+1)^(2))-root(3)((n-1)^(2))] is .

    Text Solution

    |

  8. If L=-lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

    Text Solution

    |

  9. The value of lim(x to oo ) (log(e)(log(e)x))/(e^(sqrt(x))) is .

    Text Solution

    |

  10. If lim(xto0) (1-sqrt(cos2x).root(3)(cos3x).root(4)(cos4x)...root(n)(co...

    Text Solution

    |

  11. The value of lim(x to oo ) (x-x^(2)log(e)(1+(1)/(x))) is .

    Text Solution

    |

  12. Let S(n)=1+2+3+...+n " and " P(n)=(S(2))/(S(2)-1).(S(3))/(S(3)-1).(S(4...

    Text Solution

    |

  13. If lim(xto1)(asin(x-1)+bcos(x-1)+4)/(x^(2)-1)=-2, then |a+b| is.

    Text Solution

    |

  14. Let lim(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a). Then the value of f(4) ...

    Text Solution

    |

  15. Number of integral values of k for which lim(xto1) sin^(-1)((k)/(log...

    Text Solution

    |

  16. If lim(xto1) (1+ax+bx^(2))^((e)/((x-1)))=e^(3), then the value of bc i...

    Text Solution

    |

  17. Let f''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))/...

    Text Solution

    |

  18. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then the value of 1//...

    Text Solution

    |

  19. The integer n for which lim(xto0) ((cosx-1)(cosx-e^(x)))/(x^(n)) is a ...

    Text Solution

    |

  20. If lim(xto0) [1+x+(f(x))/(x)]^(1//x)=e^(3), then the value of ln(lim(x...

    Text Solution

    |