Determine the following limits if it exists.

a. lim x-->5 (4x/x-5)

at x = 5, we get 20/0 which is undefined

The limit does not exist

(we only have work to do if the limiting value produces 0/0)

Reiny, want to help on my 2nd question I did the some of the work but I'm stuck on the last step and need guidance

go to your other post further up

To determine the limit of (4x) / (x - 5) as x approaches 5, we need to plug in 5 for x and see what happens.

1. Substitute 5 for x in the expression: (4 * 5) / (5 - 5)
2. Simplify the expression: 20 / 0

At this point, we can see that the denominator is 0. Division by 0 is undefined, which means the limit does not exist.

Therefore, the limit of (4x) / (x - 5) as x approaches 5 does not exist.