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lim(xrarr oo) (log[x])/(x) , where [x] d...

`lim_(xrarr oo) (log[x])/(x)` , where `[x]` denotes the greatest integer less than or equal to x, is

A

0

B

1

C

-1

D

non-existent

Text Solution

Verified by Experts

The correct Answer is:
A
Let `x =n+k`, where `0lt k ly 1`. Then , `[x]=n`.
` therefore lim_(xto oo) (log[x])/(x)=lim_(nto oo) (logn)/(n+k)`
` rArr lim_(xto oo) (log[x]) /(x) =lim_(nto oo) (1)/(n)=0 ["Using L'Hospital 's Rule"]`
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