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The formal definition of a unit is worthless to an engineer. It doesn't have any particular bearing on real life. As such my understanding of it is not intuitive.
I could try, but not on a Friday afternoon. Posts: 10886 | Registered: Feb 2000
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For any limit, there's two numbers. There's the number we're approaching the function of, and the number we're approaching after we take the function. A limit exists when as we approach the function of a particular number, we can come arbitrarily close to another number (as the value of the function).
So for instance, the limit of x^2 as we approach 2 is 4, because as we approach the function (x^2) of a number (2), we're approaching the number 4, and we can get as arbitrarily close to 4 as we want by getting closer and closer to 2.
We're also getting closer and closer to 5 as we approach the function (x^2) of 2 (well, if we only approach from the lower end of the number scale, which is a specific sort of limit), but we can't get arbitrarily close to it. We'll always be at least 1 away.
Limits are pretty easy to show somebody specific examples of, but hard to explain generally.
Posts: 15770 | Registered: Dec 2001
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quote:The thing that may be tripping you up in my bathtub example is that I don't offer a formula for calculating the volume in the tub at any given time. Unless you want to do some calculus (and I don't think you do ) there is no way for you to determine what the volume of water in the tub is at an arbitrary time.
It would help if I could actually remember enough calculus...
quote:If I had made this thread, I'd have called it:
"An explanation of a concept integral to my existence: the derivative"
Very cute, Bok.
I'll bet rivka has some good sources to explain limits.
[ April 10, 2005, 01:09 AM: Message edited by: Ela ]
Posts: 5771 | Registered: Nov 2000
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. . . and that was the only site I found that actually seemed aimed at teaching the concept of limits to non-math people. Found quite a few that want to sell books that would do so. Posts: 32919 | Registered: Mar 2003
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