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Fubini’s Theorem Guido Fubini, born 19 Jan 1879 in Venice, Italy, died 6 June 1943 in New York, USA, was a great mathematician that added a great theorem to the concept of calculus. Guido Fubini's father Lazzaro Fubini was a mathematics teacher at the Scuola Macchinisti in Venice. Guido Fubini came from a mathematical background and was influenced by his father towards mathematics when he was young. In 1896, Fubini entered the Scuola Normale Superiore di Pisa. There he was taught by Dini and Bianchi who quickly influenced Fubini to undertake research in geometry. He presented his doctoral thesis Clifford's parallelism in elliptic spaces in 1900. In October 1901 Fubini began teaching at the University of Catania in Sicily, and in 1908 Fubini moved to Turin where he taught both at the Politecnico and at the University of Turin. Fubini created a theorem very significant to our Calculus 3 class at Miramar college. His theorem makes it possible to change the order of integration with double integrals, which is used to find area under a plane. Fubini assumed that both integrals are less then infinite spaces. Therefore Fubini’s theorem states that if the absolute value of the function is finite, the order or integration doesn’t matter and can be reversed. If we integrate first in respect to x, then in respect to y, we get the same answer as if we integrated in terms of y first, then x. Putting dydx means that we need to re-arrange the limits of integration so the inside integral has limits for y, and the outside integral has the limits for x, and vice versa. In terms of the calculus 3 curriculum, this theorem makes it possible to evaluate double integrals in a much simpler way. This also makes it possible to change the limits of integration. This means looking at it horizontally versus horizontally, or vice versa. By graphing and visualizing we can

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## Mat 117 Research Paper

914 Words | 4 PagesYou should have. How does this number game work? You need to explain this using a variable x. Hint: Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression. How did the number game use the skill of simplifying rational expressions?

## Albert Speer Essay

1457 Words | 6 PagesOutline the main features in the background and rise to prominence of the twentieth-century personality you have studied. Albert Speer Albert Speer was a prominent figure in Hitler’s quest to build support for the Third Reich. Speer was born in Mannheim, Germany in 1905 to a wealthy middle-class family. His father was a successful architect and with his busy lifestyle Speer’s childhood lacked affection causing an emotional distance between Speer and his parents which would later have an impact on relations which Speer created in the ultimate search for a mentor. After abandoning his dream of becoming a mathematician Speer began his career in architecture and in 1923 attended the Institute of Technology in Karlsruhe, finishing his architecture course in 1927.

## Psy 315 Week 2 Math Paper

499 Words | 2 PagesJoint variation is the same thing as a direct variation with two or more quantities. Joint variation equations are solved using y=kxz. You will want to use the information of each variable to solve the equation. Once you have determined the numbers for the equation use the values and rewrite the problem. Usually you will need to find z in a typical equation.

## Exam Questions On Mathematics

625 Words | 3 PagesThis changes the now rational exponent to x^3/3, which simplified leaves x as the final answer. * The product of powers property states that exponents with the same base, when multiplied, add their exponents together. So we add the numerators up and keep the denominator to get x^3/3, which is simply x. * When a negative exponent is in the denominator as it is here, you make it bring it upward to make a positive. One times x^1 leaves x when simplified.

## Pt1420 Unit 1 Research Paper

1615 Words | 7 PagesMax or min is determined by positive or negative a sign. Vertex is (LOS, value of y when LOS is plugged in). When the equation isn’t given (word problem), (1) write a system of equations to model the problem, (2) use substitution to combine the system into a single equation, necessarily solving for the variable you are trying to maximize or minimize, (3) use line of symmetry formula to find the value that maximizes or minimizes the function, and (4) use this value to find the maximum or minimum value of the function.

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707 Words | 3 PagesHowever, you will probably also want to explore the disk images to get an intuitive sense of how they are structured. There are two good ways to interface with these images. The first way is to interact with it like a user by mounting the file system so that you can use standard commands (mkdir, cp, rm, ln) to interact with it. Details of how to do this are below. The second way is to interact with the disk as if it is a flat binary file.

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9623 Words | 39 PagesThen the result is a valid description and formula. For example, the dual of the first formula in this section reads as follows: Use the following formula to turn on the rightmost 0-bit in a word, producing all 1’s if none (e.g., 10100111 ⇒ 10101111): x | (x + 1) There is a simple test to determine whether or not a given function can be implemented with a sequence of add’s, subtract’s, and’s, or’s, and not’s [War]. We may, of course, expand the list with other instructions that can be composed from

## Albert Speer Rise to Prominence

1081 Words | 5 PagesAt school Speer excelled, particularly in mathematics. In 1923, aged 18, Speer left school with the ambition of becoming a mathematician. However, his Father disapproved and persuaded him to follow in the footsteps of himself in becoming an architect. Due to the inflation period of 1923, Speer decided to start his architectural studies locally at Karlsruhe Institute of Technology. In 1924 the stabilizing inflation rate meant Speer could transfer to the more esteemed Munich Institute of Technology and a year following that he transferred to Berlin Institute of Technology.

## Albert Speer Biography Essay

1176 Words | 5 PagesAlbert Speer was born on 19 March 1905 in Mannheim, Germany, into a solidly upper middle class which was part of the German, ‘haute bourgeosie’, the social elite. As a result, Albert Speer lived prosperously and his family even survived the hyperinflation of 1923. Albert was the second of three boys to Albert Friedrich Speer Senior, and his mother, Luise Mathilde Wilhelmine Hommel. Although Albert Speer was quite a mathematician, his parents persuaded him to take the path of architecture. Speer studied at the technical schools in Karlsruhe, Munich and Berlin, and graduated as an architect in 1927 at the Technical University of Berlin.

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