The given expression is the limit of the greatest integer function (also known as the floor function) as x approaches 9.

The greatest integer function, denoted as [[x]], gives the largest integer less than or equal to x.

So, as x approaches 9 from the left (i.e., values slightly less than 9), the greatest integer less than or equal to x is 8.

As x approaches 9 from the right (i.e., values slightly more than 9), the greatest integer less than or equal to x is 9.

Since the left-hand limit (8) and the right-hand limit (9) are not equal, the limit of the function as x approaches 9 does not exist.

Question

The given expression is the limit of the greatest integer function (also known as the floor function) as x approaches 9.

The greatest integer function, denoted as [[x]], gives the largest integer less than or equal to x.

So, as x approaches 9 from the left (i.e., values slightly less than 9), the greatest integer less than or equal to x is 8.

As x approaches 9 from the right (i.e., values slightly more than 9), the greatest integer less than or equal to x is 9.

Since the left-hand limit (8) and the right-hand limit (9) are not equal, the limit of the function as x approaches 9 does not exist.

Knowee AI · Accepted Answer

The given expression is the limit of the greatest integer function (also known as the floor function) as x approaches 9.

The greatest integer function, denoted as [[x]], gives the largest integer less than or equal to x.

So, as x approaches 9 from the left (i.e., values slightly less than 9), the greatest integer less than or equal to x is 8.

As x approaches 9 from the right (i.e., values slightly more than 9), the greatest integer less than or equal to x is 9.

Since the left-hand limit (8) and the right-hand limit (9) are not equal, the limit of the function as x approaches 9 does not exist.

lim⁡𝑥→9[[𝑥]]=x→9lim [[x]]=