If [x] is the greatest integer not greater than x, then determine the limit of [x ]when x goes to (1/2) is it exists
Here, we have (greatest integer function)
The graph of this function looks like this:-
Here, we want to find
Here we calculate LHL and RHL separately.
LHL:-
(As here x approaches from left and so, [x] is 0)
RHL:-
(As here x approaches from right and so, [x] is 0)
As LHL=RHL=0 , we know the limit exists and is:-
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