lim𝑥→92[[𝑥]]=x→ 29 lim [[x]]=(Remember that [[𝑥]][[x]] represents the greatest interger function of x.)
Question
lim𝑥→92[[𝑥]]=x→ 29 lim [[x]]=(Remember that [[𝑥]][[x]] represents the greatest interger function of x.)
Solution
The greatest integer function, also known as the floor function, gives the largest integer less than or equal to x.
As x approaches 9 from the left (x -> 9^-), the greatest integer function [[x]] will be 8, because 8 is the largest integer less than 9.
As x approaches 9 from the right (x -> 9^+), the greatest integer function [[x]] will be 9, because x is now greater than or equal to 9.
Therefore, the limit of the greatest integer function as x approaches 9 does not exist because the left-hand limit (8) does not equal the right-hand limit (9).
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