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If f (x) =lim (x to oo) x ((3)/(2) + [co...

If `f (x) =lim _(x to oo) x ((3)/(2) + [cos x)(sqrt(n^(2) +1)-sqrt(n ^(2) -3n +1)))` where [y] denotes largest integer `le y,` then identify the correct statement (s).

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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