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For each t in R let [t] be the greatest ...

For each `t in R` let `[t]` be the greatest integer less than or equal to t then `lim_(xrarr0^+)x([1/x]+[2/x]+...+[15/x])` (1) is equal to 0 (2) is equal to 15 (3) is equal to 120 (4) does not exist (in R)

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  • For each x in R , let [x] be the greatest integer less than or equal to x, Then, lim_( x to 0^(-)) ( x ([x] + | x| ) sin [x]) / ([x]) is equal to

    A
    0
    B
    sin 1
    C
    `-sin 1`
    D
    1

  • if [x] denotes the greatest integer less than or equal to x, than lim_(xrarr0)(x[x])/(sin|x|) , is

    A
    0
    B
    1
    C
    non-existant
    D
    none of these

  • For each x in R , let [x]be the greatest integer less than or equal to x. Then lim_(xto1^+) (x([x]+absx)sin[x])/absx is equal to

    A
    `-sin 1`
    B
    0
    C
    1
    D
    sin 1

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    For each t in R ,let[t]be the greatest integer less than or equal to t. Then lim_(xto1^+)((1-absx+sinabs(1-x))sin(pi/2[1-x]))/(abs(1-x)[1-x])

    If [ x ] denotes the greatest integer less than or equal to x, then the value of lim_(x to 0) (1-x +[x-1] + [1-x]) is:

    Let [x] denote the greatest integer less than or equal to x for any real number x. then lim_(xrarroo)([nsqrt2])/(n) is equal to

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