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If [.] denotes the greatest integer func...

If `[.]` denotes the greatest integer function , then `lim_(xrarr0) sin[-sec^2x]/(1+[cos x ])` is equal to

A

`sin 1`

B

`-sin1`

C

`sin2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`lim_(xto0^-) sin[-sec^2x]/(1+[cos x ])=(sin(-2))/(1+0)=-sin2`
and, `lim_(xto0^+)(sin[-sec^2x])/(1+[cosx]) =(sin(-2))/(1+0)=-sin2`
`therefore lim_(xto0^-)(sin[-sec^2x])/(1+[cosx])=lim_(xto0^+)(sin[-sec^2x])/(1+[cosx])=-sin2`
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