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kelcharge

Use for limits?

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I am just starting to study limits and points of tangency in my Calc. book. The only thing is, I can't figure out what limits would be used for, in real life or game programming. Could any one let me know what a limit can be used for?

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Limits are the foundation of derivatives and integrals. With out them calculus wouldn't exist.

Limits can be used for a lot of things. I was designing a server less chat network a while ago (I'm not skilled enough to implement it) and the way people connected made a specific pattern. Using this pattern and limits I was able to calculate the number of connections needed for the network to work.

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yes, limits are the foundation of calculus. but also find use in series. infinite series representations of functions. which provide us with usefull approximations to functions. they rear there head up all over the place and no thouro understanding of calculus, dirrerentiablitiy, continunity can exist with out a good grasp on the limit, at least in the intuitive context. I think a good intuitive understanding of them is very essential. but knowing all the little tricks to solve them, maybe not as usefull, but certinally helpfull.

Tim <- "calculus lover"

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Calculus is important in physics. In particular, understanding integrals and derivatives in terms of limits is very important. Translating a problem into equations requires an understanding of limits, as does properly applying numeric techniques to those equations (when they aren't solvable by analytic methods).

This is as opposed to mathematics, where a higher level understanding of integrals and derivatives is more important.

Also, look at the thread "Formal definition of the integral?" (it's on the second page of this forum at the moment).

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Original post by mike25025
Limits are the foundation of derivatives and integrals. With out them calculus wouldn't exist.

This is most certainly not true since the concept of limit did not come into existance with any kind of rigour till the time of Cauchy, over a century after the fluxions of Newton and infinitesimals of Leibniz.

In fact, using the construction of hyperreal numbers and the principle of extension (plus one or two other fancy words that will interest no one but a mathematician) one can develop the calculus without the need for limits as a basis by the consistent (i.e. not naive, rigorous) use of infinitesimals.

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Original post by Anonymous Poster
Quote:
Original post by mike25025
Limits are the foundation of derivatives and integrals. With out them calculus wouldn't exist.

This is most certainly not true since the concept of limit did not come into existance with any kind of rigour till the time of Cauchy, over a century after the fluxions of Newton and infinitesimals of Leibniz.

In fact, using the construction of hyperreal numbers and the principle of extension (plus one or two other fancy words that will interest no one but a mathematician) one can develop the calculus without the need for limits as a basis by the consistent (i.e. not naive, rigorous) use of infinitesimals.

It's true that infinitesimals were originally used in formulating the calculus, but infinitesimals themselves are best defined in terms of limits. (In fact, AFAIK one can consider the two concepts as almost perfectly interchangeable). (I'm sure you know this... it's more for the benefit of the OP).

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Original post by timw
yes, limits are the foundation of calculus. but also find use in series. infinite series representations of functions. which provide us with usefull approximations to functions. they rear there head up all over the place and no thouro understanding of calculus, dirrerentiablitiy, continunity can exist with out a good grasp on the limit, at least in the intuitive context. I think a good intuitive understanding of them is very essential. but knowing all the little tricks to solve them, maybe not as usefull, but certinally helpfull.

Tim <- "calculus lover"


I disagree with this. In fact, I feel the exact opposite: for a beginner, limits get in the way of an "intuitive grasp" of the calculus of differentiation and integration. One needs nothing more than an intuitive understanding of limits (that which common sense dictates) and that of infinitesimals. I suscribe to the "new school" of a mathematics view, more conventional traditionists may disagree with me.

------I am the same Anonymous poster as above-----

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Original post by Sneftel
Quote:
Original post by Anonymous Poster
Quote:
Original post by mike25025
Limits are the foundation of derivatives and integrals. With out them calculus wouldn't exist.

This is most certainly not true since the concept of limit did not come into existance with any kind of rigour till the time of Cauchy, over a century after the fluxions of Newton and infinitesimals of Leibniz.

In fact, using the construction of hyperreal numbers and the principle of extension (plus one or two other fancy words that will interest no one but a mathematician) one can develop the calculus without the need for limits as a basis by the consistent (i.e. not naive, rigorous) use of infinitesimals.

It's true that infinitesimals were originally used in formulating the calculus, but infinitesimals themselves are best defined in terms of limits. (In fact, AFAIK one can consider the two concepts as almost perfectly interchangeable). (I'm sure you know this... it's more for the benefit of the OP).


Hello, you misunderstand me, I do not mean the naive/intuitive calculus of old but the more modern vesion based on hyperreal numbers

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Guest Anonymous Poster
http://shop.store.yahoo.com/doverpublications/0486428869.html

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Quote:
Original post by kelcharge
I am just starting to study limits and points of tangency in my Calc. book. The only thing is, I can't figure out what limits would be used for, in real life or game programming. Could any one let me know what a limit can be used for?


On the side of differentiation: limits let us define & talk about how fast something is happening NOW, rather than (merely) how fast on average something happens over a time interval.

On the side of integration: limits let us define & talk about, well, area.

I'll leave it to everyone's imagination the uses to which these two items, rate of change, and area, can be put.

In terms of mathematics-education, limits represent the beginning of "real math", rather than "hooked on phonics" math. More or less.

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