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If f(x)=(lim)(nvecoo)(3/2+[cosx](sqrt(n...

If `f(x)=(lim)_(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1)))` where `[y]` denotes largest integer `lt=,` then identify the correct statement(s). `("lim")_(nvecoo)f(x)=0` `("lim")_(nvecpi/2)f(x)=(3pi)/4` `f(x)=(3x)/2AAx in [0,pi/2]` `f(x)=0AAx in (pi/2,(3pi)/2)`

A

`lim _(xto 0) f (x)=0`

B

`lim _(x (pi)/(2)) f(x) =(3pi)/(4)`

C

`f (x) =(3pi)/(2)AA x in [0, (pi)/(2)]`

D

`f (x)= 0 AA x in ((pi)/(2), (3pi)/(2))`

Text Solution

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The correct Answer is:
A, C, D
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