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Limit - Applications

limits real calculus interval

The limit concept is essential to understanding the real number system and its distinguishing characteristics. In one sense real numbers can be defined as the numbers that are the limits of convergent sequences of rational numbers. One application of the concept of limits is on the derivative. The derivative is a rate of flow or change, and can be computed based on some limits concepts. Limits are also key to calculating intergrals (expressions of areas). The integral calculates the entire area of a region by summing up an infinite number of small pieces of it. Limits are also part of the iterative process. An iteration is repeatedly performing a routine, using the output of one step as the input of the next step. Each output is an iterate. Some successful iterates can get as close as desired to a theoretically exact value.


Resources

Books

Abbot, P., and M.E. Wardle. Teach Yourself Calculus. Lincolnwood: NTC Publishing, 1992.

Allen, G.D., C. Chui, and B. Perry. Elements of Calculus. 2nd ed. Pacific Grove: Brooks/Cole Publishing Co., 1989.

Gowar, Norman. An Invitation to Mathematics. New York: Oxford University Press, 1979.

Larson, Ron. Calculus With Analytic Geometry. Boston: Houghton Mifflin College, 2002.

Silverman, Richard A. Essential Calculus With Applications. New York: Dover, 1989.

Periodicals

McLaughlin, William I. "Resolving Zeno's Paradoxes." Scientific American 271 (1994): 84-89.


J. R. Maddocks

KEY TERMS

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Converge

—To converge is to approach a limit that has a finite value.

Interval

—An interval is a subset of the real numbers corresponding to a line segment of finite length, and including all the real numbers between its end points. An interval is closed if the endpoints are included and open if they are not.

Real Number

—The set of numbers containing the integers and all the decimals including both the repeating and nonrepeating decimals.

Sequence

—A sequence is a series of terms, in which each successive term is related to the one before it by a fixed formula.

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3 months ago

My question was always with using integrls in real life. I understand how to correctly solve problems but is there any real life problems that I can use on this, as a future electrical engineer I would need to how to actually apply this to a rel life porblem, my teachers has only given me bullshit problems to solve and none of them really came with a story so I have nothing to rlate this to. Any of you out there nice enough to explain how to understand this better? Im currently in china so I don't have any access to any good american sites, that is why i am on here, so any help would bre appriated! and also does anyone know the use of the rose pedals? overall I believe that I can become the next einstin since I just solve the important mystery of time travel, as soon as this is posted I will know who responded and when they responded, and that is because I am the one who don't need a gun to get respect from up on the street. So any help would be appreciated.