| 词汇 | mean-value-theorem |
| 释义 | BETA mean value theoremcollocation in Englishmeanings of mean, valueand theoremThese words are often used together. Click on the links below to explore the meanings. mean noun[ S ] uk /miːn/ us /miːn/ mathematics specialized the result you get by adding two or more amounts together and dividing the total by the number ... See more at mean value noun uk /ˈvæl.juː/ us /ˈvæl.juː/ the amount of money that can be received ... See more at value theorem noun[ C ] uk /ˈθɪə.rəm/ us /ˈθiː.rəm/ (especially in mathematics) a formal statement that can be shown to be true ... See more at theorem Examples of mean value theoremmean value theorem It can be generalized to more variables according by the meanvaluetheorem for divided differences. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since x 0 for the meanvaluetheorem to work then we may conclude that f(x) - g(x) 0. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He also refined the second meanvaluetheorem of integration. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. By applying the meanvaluetheorem, the operator can deduce that the vehicle's speed must equal its average speed at some time between the measurements. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In practice, what the meanvaluetheorem does is control a function in terms of its derivative. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. From the meanvaluetheorem, we know that the vehicle's speed must equal its average speed at some time between the measurements. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If is additionally assumed to be "continuously" differentiable, then the claim can be proved by applying the meanvaluetheorem and converting the sum into an integral. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Therefore, has to be constant on, because otherwise we would obtain a contradiction to the mean valuetheorem (applied separately to the real and imaginary part in the complex-valued case). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These order-theoretic properties lead to a number of important results in real analysis, such as the monotone convergence theorem, the intermediate value theorem and the meanvaluetheorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Next, we employ the meanvaluetheorem. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Because acceleration also varies with time, however, the extended meanvaluetheorem must also be extended to the second time derivative to obtain the correct displacement. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. He worked on functional analysis, harmonic analysis, ergodic theory, mean value theorems, and numerical integration. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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