Find the limit with the help of the squeeze theorem.
, where indicates the Floor Function.
Note the following important points:
The Sandwich theorem also known as squeeze play theorem applicable for any three real valued functions and that shares the same domain such that for in the domain of definition states the following: For some real value of , if ,then
From the definition of GIF, the following is evident.
--------(i)
Now, multiply the inequality (i) by the reciprocal of that still preserves the inequality.
--------------(ii)
Apply the squeeze theorem to the inequality (ii).
Therefore, the required value of the limit is
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