Find the value of 5lim⁡𝑥→13+⌊𝑥⌋−3lim⁡𝑥→3−⌊𝑥⌋5 x→13 + lim​ ⌊x⌋−3 x→3 − lim​ ⌊x⌋, where ⌊𝑥⌋⌊x⌋ denotes the greatest integer less than or equal to 𝑥x.

The given expression is 5lim(x→13) [⌊x⌋] - 3lim(x→3) [⌊x⌋].

The greatest integer function, also known as the floor function, gives the largest integer less than or equal to x.

Step 1: Evaluate the limits separately.

For the first limit, as x approaches 13, the greatest integer less than or equal to x is 13. So, lim(x→13) [⌊x⌋] = 13.

For the second limit, as x approaches 3, the greatest integer less than or equal to x is 3. So, lim(x→3) [⌊x⌋] = 3.

Step 2: Substitute the values of the limits into the expression.

= 513 - 33 = 65 - 9 = 56

So, the value of the given expression is 56.