GutZ Posted April 16, 2009 Posted April 16, 2009 I think this is one of the things that calculus screws my train of thought on. I think I understand what a limit is. Why would you have to define a limit? Is there ever a situation where not defining a limit would change the outcome?
Cap'n Refsmmat Posted April 16, 2009 Posted April 16, 2009 What exactly do you mean? Are you asking why one would define a limit instead of just trying to solve the problem without a limit?
GutZ Posted April 16, 2009 Author Posted April 16, 2009 pretty much yeah If a function is going to go towards something regardless.....
Cap'n Refsmmat Posted April 16, 2009 Posted April 16, 2009 How about a function like [math]f(x) = \frac{x^2 - 4}{x+2}[/math] Find f(-2). The function doesn't exist at all at x = -2, but with a limit you can find what that function would be at x = -2.
Mr Skeptic Posted April 16, 2009 Posted April 16, 2009 Most of the time, you don't need to worry about limits. But both derivatives and integrals are based on limits, and to use them you need a formal, mathematically precise definition for limits or you might as well not be doing math.
Bignose Posted April 16, 2009 Posted April 16, 2009 But both derivatives and integrals are based on limits This is it right here. This is the whole point of learning limits, because the basic definitions in calculus depend on that definition. If it isn't clear now, it should become clear in the near future.
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