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Rene Descartes

20. What is t...

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20. What is the Newton-Leibniz Formula?

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Q. Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus. Leibniz developed closely analogous concepts and techniques. It has traditionally been thought that these discoveries were independent. Researchers have, however, recently discovered notes of Leibniz’ that discuss one of Newton’s books on mathematics. Several scholars have argued that since the book includes a presentation of Newton’s calculus concepts and techniques and since the notes were written before Leibniz’ own development of calculus concepts and techniques, it is virtually certain that the traditional view is false. A more cautious conclusion than this is called for, however. Leibniz’ notes are limited to early sections of Newton’s book; sections that precede the ones in which Newton’s calculus concepts and techniques are presented. In the historian’s reasoning, the two boldfaced portions play which of the following roles?

Q. The Newton-Raphson iteration formula for finding

\sqrt[3]{c}

where c > 0 is,

Q. The formula proposed by Newton for velocity of sound in air is based on _________ process.

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