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Real Exponents
Real Exponents

... (since 2x is an increasing function for rational x). Also, since 2 < 2, the sequence of approximations are all less than 22 = 4. A basic ...
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... 9. An appliance store manager estimates that for x television ads run per day, R( x)  0.01x3  x 2  3x  200 refrigerators will be sold per month. Find R (4) and interpret what it tells us about sales. A) R (4)  4.52; sales will be increasing at about 5 refrigerators per month per ...
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... In the present note we shall give two proofs of a property of the poly-Bernoulli numbers, the closed formula for negative index poly-Bernoulli numbers given by Arakawa and Kaneko [1]. The first proof uses weighted Stirling numbers of the second kind (see [2], [3]). The second, much simpler, proof is ...
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Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century.""
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