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Derivatives and Definite Integrals
Word Count (excluding title and works cited page): 628
Calculus pioneers of the seventeenth century such as Leibniz, Newton, Barrow, Fermat, Pascal, Cavelieri, and Wallis sought to find solutions to puzzling mathematical problems. Specifically, they expressed the functions for derivatives and definite integrals. Their areas of interest involved discussions on tangents, velocity and acceleration, maximums and minimums, and area. This introductory paper shall briefly introduce four specific questions related to these problems and the solutions that were sought.
In calculus, how a function changes in response to input is measured using a derivative. The derivative of a function is the result of mathematical differentiation. It measures the instantaneous rate of change of one certain quantity in relationship to another and is expressed as df (x)/dx. It can be interpreted geometrically as the slope of the curve of a mathematical function f (x) plotted as a function of x. The integral of a function...
To do this, mathematicians use tangent and secant lines. Segments drawn in tangent to or through a curved line create angles which help define and measure the slope of a curve. The slope of a curve is found at a point. The method is to draw a secant line through that point and to first find the slope of the secant line. The formula is ?y/?x. The next step is to slide the second point along the curve toward the first. The secant approaches the limit and, as the two points meet, it becomes a tangent line. The slope of the tangent becomes the slope of the curve and is called the derivative. It is written dy/dx .
How are derivatives used to solve velocity and acceleration problems? Another common use of derivatives is the ability…
Nave, R. Derivatives and integrals. Hyper Physics, Retrieved from http://hyperphysics.phy-astr.gsu.edu
Kouba, D.A. The Calculus Page, U.C. Davis Department of Mathematics. http://www.math.ucdavis.edu, Retrieved January 25, 2011
Weisstein, E. Wolfram Mathworld. http://mathworld.wolfram.com, Retrieved January 25, 2011
Calculus and Definitions of Its Concepts Indefinite integration Indefinite integration is the act of reversing any process of differentiation. It is the process of obtaining a function from its derivative. It is also called anti-derivative of f. A function F. is an anti-derivative of f on an interval I, if F'(x) = f (x) for all x in I. A function of F (x) for which F'(x)=f (x), this means that for
(Hilton, 26) in general, no mathematician would be willing to accept the solution to a problem without some sort of proof, and in the same way, no student of calculus would be ready to accept the resolution of a problem without the necessary proof. (Cadena; Travis; Norman, 77) It must be stated that Newton's mathematics that involved 'fluxions' was one of the first forms of the area defined as 'differential
……South African Municipalities Municipal Revenue Loss Reduction through Improved Municipal Valuation Methodologies:Balance Sheet Enhancement of South African Municipalities to Improve Rates and Taxes Revenue GenerationAbstractThis study examines the property valuation process of Municipalities in South Africa and develops a strategy for strengthening that process in order to more efficiently value properties and ultimately to enhance municipal balance sheets and increase revenue streams. This study proposes an innovative valuation method based
The is also based on drive-defence model which was advanced by Freud. The second topology one includes the less common dreams whose meaning are different and should therefore be treated and handled in the light of latest theoretical frameworks as advanced by Kohut Self-psychology. He referred to these dreams as "Self-state dreams" which are experienced when the patient's psychological structure stability is in jeopardy .Such crisis or threat usually occur
govern the profitability of banks in the South Easter part of Europe. The banking profitability in question is evaluated in terms of the rate of Return on Assets (ROA) and the rate of Return on Equity (ROE) .These two measures are expressed in terms of various other determinants. This paper therefore makes use of a series of raw data collected from South Eastern Europe credit institutions over a five-year