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If U(n)=(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)...

If `U_(n)=(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))^(2).............(1+(n^(2))/(n^(2)))^(n)`m then `lim_(n to oo)(U_(n))^((-4)/(n^(2)))` is equal to

A

`(4)/(e )`

B

`(16)/(e^(2))`

C

`(e^(2))/(16)`

D

`(4)/(e^(2))`

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Knowledge Check

  • lim_(n rarr oo) II_(n=2)^(n) (1 - (3)/(n (n+2))) is equal to

    A
    1
    B
    4
    C
    `(1)/(4)`
    D
    `(3)/(4)`

  • lim_(ntooo) ((n^(2)-n+1)/(n^(2)-n-1))^(n(n-1)) is equal to

    A
    `underset(xto0)lim([x+|x|])/(x)=0`, where `[x]` denotes the greatest integer functions.
    B
    `underset(xto0)lim(xe^((1)/(x)))/(1+e^((1)/(x)))=0`
    C
    `underset(xto3)lim(x-3)^((1)/(5))sgn(x-3)=0`, where sgn stands for signum function.
    D
    `underset(xto0)lim(tan^(-1)|x|)/(x)=0`

  • lim_(n to oo) ((2n^(2)-3)/(2n^(2)-n+1))^((n^(2)-1)/(n)) is equal to

    A
    `(1)/(sqrt(e ))`
    B
    `sqrt(e )`
    C
    e
    D
    `(1)/(e )`
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