Is the following a good example of a limit: See Additional details?

Question

1 pump can empty a room full of water in 24 hours, while 2 can empty it in 12 hours, 3 pumps in 8 hours. if you keep increasing the number of pumps, the time it takes to empty will approach zero, but never reach it. Is this a valid analogy?

Answer 1

It's not an analogy at all. It is an example of a particular limiting process. What you need to be clear about is the underlying process you're describing. In other words, the limit, as the number of pumps increases without bound, of the time it takes to empty the room of water, is zero.

Answer 2

Just for kicks, I'd like to point out that a limit problem doesn't have to be the only way to solve a problem. For instance, the lim as x approaches 2 of y=2x+67 is 71. The limit exists, the solution exists.

The limit just just happens approximate an answer when there is no actual solution.

Answer 3

I don't believe so. Even though you keep increasing the amount of the pumps, the room will eventually be drained.

A better example might be a tennis and/or a rubber ball. The ball bounces about 1/3 of it's original height. This will eventually keep going until it looks like it stopped bouncing. Even though the ball "looks" like it stopped bouncing, the ball is still bouncing, but it is so significantly small, it doesn't appear to be bouncing.

Does this make sense?

Answer 4

spb 1968 said it best, its not analogy it is infact a limit problem. The limit is 0, the room will never be instantly drained of all the water. its a good example of a limiting problem, but not an analogy!

Answer 5

yes

Answer 6

Yes, it is.

^_^

Answer 7

sure