LogFAQs > #929249460

Alternatively, you could have used L'Hopital's Rule in order to conclude that the limit is indeed four, but you probably will not learn that until your next semester. Or you could have done it via delta-epsilon proof (let epsilon = delta). Let epsilon be positive and set delta = epsilon. Then if |x - 2| < delta, then |(x^2-4)/(x-2)-4| = |(x + 2) - 4| < |x - 2| < delta = epsilon. This is the proper definition of the limit, which you might lightly touch on at the end of the limits sequence of your course. Although, it's not like I stated it properly or anything. All I did was just do a bunch of algebra and show you how the proof method works. The idea is this, I think: You can make f(x) (for x within a certain distance of, but not equal to, x = 2) as close to 4 as you like, provided you choose a sufficient distance (possibly dependent on the degree of closeness of f(x) to 4). I'm sure I didn't explain it properly, but you can find a better explanation in a textbook or online, or something. Anyway, in Advanced Calculus I, you'll be using this proof method far more often.
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