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What Did Isaac Barrow Do?
He is responsible for the FTC, or fundamental theorem of calculus.
What is fundamental about the Fundamental Theorem of Calculus?
Calculus consists of two main topics -- differentiation and integration. Differentiation is concerned with 'rates of change', for example the rate at which the position of a moving object is changing with respect to time, otherwise known as velocity. Integration is concerning with computing areas,volumes, and lenght by first approximating the region as the sum of many smaller regions which are simpler to compute, and taking the limit as the number of smaller regions increases to infinity.At first sight, it doesn't seem like these two topics -- differentiation and integration -- have anything to do with one another. In fact, in a calculus course either one could be presented first since it wouldn't require knowledge of the other one (traditionally, differentiation is taught first, then integration, but it isn't necessary to do them in this order.)However, the amazing fact is that these two seemingly unrelated problems are completely intertwined. The Fundamental Theorem of Calculus, one of the most amazing and profound results in all of mathematics, spells out just how the processes of differentiation and integration are related -- they are essentially reverse operations of one another, or two sides of the same coin. The Fundamental Theorem of Calculus is so named because it ties together the two main themes of the subject. F(x) = f (t)dt is a function then we have = f(t)dt but since Since dt = h we have - f (x) = f (t) - f(x)dt . and using the continuity of F(t), we have the following equality. - f (x) = 0 .Now, the punch line!The function F(x) is differentiable and F '(x) = f (x).Many calculus books have two parts to the FTC (Fundamental Theorem of Calculus)Part one states that the area under a section of a curve is the antiderivative evaulated at the upper limit minus the lower limit. That is:Integral ( f(x) dx) from a to b = F(b) - F(a)where b is the upper boundary and a is the lower boundaryandPart two states that the derivate of integration is the integrand:d/dx integral (f(t) dt) from 0 to x = f(x)where x is the upper boundary and 0 is the lower boundary.So what went into the integral that you derive is the result.Note: it really helps to see the pictures of what is going on.
How is the AP Calculus AB Test Scored?
Calculus AB is the branch of the calculus curriculum offered by the College Board exam administration. It differs from its counterpart, Calculus BC, in that AB only covers material into a standard "college" introductory calculus course.Usually, Calculus AB corresponds to a typical university's Calculus I course (or similarly named). In contrast, BC is a more accelerated course which covers material that corresponds to both Calculus I and II. This may vary depending on the university, as some combine both Calculus I and II into one course, in which case AB would only cover one semester of material.Calculus AB includes content based on limits, continuity, differentiation, integration, the IVT, the MVT, the EVT, and the FTC.
What does the FTC have to say about warranty?
Answering "What does the FTC have to say about warranty?"
When was FTC Fiľakovo created?
FTC Fiľakovo was created in 1908.
What is 'FTC' when referring to cooking?
All I know is that FTC stands for Fedreal Trade Commission
How do you solve the limits of a definite integral?
By using the fundamental theorem of Calculus. i.e. The integral of f(x) = F(x), your limits are [a,b]. Solve: F(b) - F(a). The FTC, second part, says that if f is a continuous real valued function of [a,b] then the integral from a to b of f(x)= F(b) - F(a) where F is any antiderivative of f, that is, a function such that F'(x) = f(x). Example: Evaluate the integral form -2 to 3 of x^2. The integral form -2 to 3 of x^2 = F(-2) - F(3) = -2^3/3 - 3^3/3 = -8/3 - 27/3 = -35/3
How does the FTC regulate antitrust?
(FTC) and the Antitrust Division of the U.S. Department of Justice enforce antitrust laws. The FTC has the power to temporarily stop companies from employing suspected anti-competitive practices
What does the FTC regulate?
fruit
What does the letter T stand for in the letters FTC?
In the United States, "the FTC" typically refers to the Federal Trade Commission.
What can be found on the FTC GOV website?
FTC stands for Federal Trade Commission, and 'FTC GOV' is the name of their website. The Federal Trade Commission serves the public with information about consumer protection and identity theft.
What does the letters FtC mean on the inside of a ring?
FtC would refer to a registered trademark of the company that produced the ring. There are many companies which use FTC in their trademarks. USPTO dot gov has a trademark search function available.
