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The value o lim(xtooo)(1/(n^(3)))([1^(2)...

The value o `lim_(xtooo)(1/(n^(3)))([1^(2)x+1^(2)]+[2^(2)x+2^(2)]+…..+[n^(2)x+n^(2)])` is where [.] denotes the greatest integer function.

A

`x/3`

B

`x+1/3`

C

`x/3+1/3`

D

None of these

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Knowledge Check

  • int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

    A
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    B
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    B
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    C
    `(1)/(2)`
    D
    `(2)/(3)`

  • The value of int_(0)^(2)[x^(2)-1]dx , where [x] denotes the greatest integer function, is given by:

    A
    `3-sqrt(3)-sqrt(2)`
    B
    2
    C
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    D
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