The value of ("lim")(xvec0)([(100 x)/(si...

The value of `("lim")_(xvec0)([(100 x)/(sinx)]+[(99sinx)/x])` (where [.] represents the greatest integral function) is 199 (b) 198 (c) 0 (d) none of these

A

`199`

B

`198`

C

`0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

We know that
`x gt sin x " for all " x gt 0`
and , `xlt sin x " for all " x lt 0`
`rArr (x)/(sin x) gt 1 and (sin x) /(x) lt 1 " for all " x ne 0`
` rArr (100x)/(sinx) gt 100 and (99sin x) /(x) ne 0 " for all " x ne 0`
` therefore lim_(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)])=lim_(xto0) (100 +98)=198`

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