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Who invented the pythegorean theorem?
Actually, the theorem has been used long ago before mathematician called Pythagoras came along. It was previously already applied in Indian society. The theorem only came to be known as "Pythagoras Theorem" because he (or his students) were the first ones to construct a proof for the theorem.
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.
Is elementary calculus the same as calculus?
Pre-calculus refers to concepts that need to be learned before, or as a prerequisite to studying calculus, so no. First one studies pre-calculus then elementary calculus.
How do you solve this question Integrate sinz from z 1 i to 20 30i?
1) First you get the anti-derivative of sin z. This one is easy; you can look it up in the most basic standard tables of integrals. 2) Use the fundamental theorem of calculus: a. Calculate the antiderivative function for the upper limit. b. Calculate the antiderivative function for the lower limit. c. Subtract the answer of part "a" minus the answer of part "b".
Determine whether the Mean Value Theorem can be applied Then find all values of c that satisfy the theorem y equals 2 cos x plus cox 2x on 0 to π?
The mean value theorem can be applied to all continuous functions (or expressions), and so it is applicable here. There is no equation in te question and furthermore, no c (other than the first letter of cos in the expression so there are no values for c to satisfy anything!
What is the proof for theorem 1.20?
There is no theorem with the standard name "1.20". This is probably a non-standard name from a textbook which is either the 20th theorem in the first chapter or a theorem of the 20th section of the first chapter.
When was calculus first developed?
Based on the history, calculus was first developed by Sir Issac Newton in 1665-1667.
Difference between first and second shifting theorem?
Difference between first shifting and second shifting theorem
20 applications of vector analysis to solve real life problems?
Pretty much everything can be applied to calculus, and calculus to everything. If you have ever read the novel "Halo" you can see (in the first book) that Master Chief, had forgotten how much gravity was on the space-craft, and used calculus to determine the acceleration of gravity by timing the drop of a bolt and figuring out everything else. Calculus is especially important for any kind of profession that involves projectiles.
What has the author Jeffrey W Hickox written?
Jeffrey W. Hickox has written: 'First term attrition of fundamental applied skills training (Fast) students'
Who had the pythagorean theorem first?
Since the Pythagorean theorem is named after the Greek mathematician Pythagoras, it was reasonable to assume that he is the first person to have it.
What is the relationship between Isaac Newton and the branch of mathematics called Calculus?
Newton is generally taken to have been one of the two inventors of the calculus, the other being Leibniz. They worked independently, had different motivations, and used different notations. The dates are 1666 for Newton's first work on the calculus and about 1672 for Leibniz, though neither published their work until much later. The key realisation that both Newton and Leibniz had was that differentiation and integration are inverse processes. This means that areas under curves can be obtained by using anti-derivatives, a result now called the Fundamental Theorem of Calculus. This led to a systematic symbolic process for solving many problems, called at first "infinitesimal calculus" and later just "calculus". Differentiation is to do with tangents, and integration is to do with areas. Work on both tangents and areas goes back as far as the ancient Greeks (Euclid and Archimedes). The significance of the work of Newton and Leibniz was that they were the first people to really understand and exploit the connection between tangents and areas.
