Fundamental Theorem Of Calculus

Hayley
March 17, 2010
Thesis

Fundamental Theorem of cream of tartar
Calculus is a branch of maths which focuses on dividing lines, integrals, differential gears, functions, and infinite series. It utilizes many different forms of mathematics such as: geometry, algebra, trigonometry, etc. however potassium hydrogen tartrate can be broken down into two main branches: differential calculus and integral calculus. While there atomic number 18 many operose and useful theorems in the wide spectrum of calculus, there is one in particular of great importance, the Fundamental Theorem of Calculus. This theorem is often described as pioneering and perhaps one of the greatest theorems in the history of Mathematics. But what is the Fundamental Theorem of Calculus? And why is it helpful?
The Fundamental Theorem of Calculus deals with integrals or anti-derivatives. In order to understand what an integral is or how to take an integral one must understand the conceit of a derivative or differentiation. A derivative is the instantaneous rate of change of y with respect to x. When a derivative is taken what we settle is the be given of the sunburn line to a graph at the place P. We can approximate the slant by drawing a line through the point P and another point nearby, and then finding the slope of that line, called a secant line.




b-ya-x=?y?x=fx+?x-f(x)?x (Kline, 1967)
consequently we must choose a random interval to be ?x. How does the size of ?x affect our estimate of the slope of the tangent line? The smaller ?x is, the more accurate this idea is. What we want to do is decrease the size of ?x as much as possible. We do this by taking the limit as Delta-x approaches zero. In the limit, assuming the limit exists, we will find the exact slope of the tangent line to the curve at the given point. This value is the derivative:
dfdx=lim?x?0fx+?x-f(x)?x (Kline, 1967)
The equation above is the formal definition of a derivative. There are many rules to differentiation and in order to get a good grasp on...If you want to get a fully essay, order it on our website: Ordercustompaper.com



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