BETA
Examples ofmean value theorem
Dictionary> Examples ofmean value theorem
mean value theoremisn’t in the Cambridge Dictionary yet. You can help!
Add a definition
It can be generalized to more variables according by themeanvaluetheoremfor divided differences.
From
This example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Since x 0 for themeanvaluetheoremto work then we may conclude that f(x) - g(x) 0.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.He also refined the secondmeanvaluetheoremof integration.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.By applying themeanvaluetheorem, the operator can deduce that the vehicle's speed must equal its average speed at some time between the measurements.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.In practice, what themeanvaluetheoremdoes is control a function in terms of its derivative.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.From themeanvaluetheorem, we know that the vehicle's speed must equal its average speed at some time between the measurements.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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 themeanvaluetheoremand converting the sum into an integral.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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 meanvaluetheorem(applied separately to the real and imaginary part in the complex-valued case).
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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 themeanvaluetheorem.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Next, we employ themeanvaluetheorem.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Because acceleration also varies with time, however, the extendedmeanvaluetheoremmust also be extended to the second time derivative to obtain the correct displacement.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
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.
- watchful eye
- watchfully
- watchfulness
- watchful waiting
- watchful-waiting
- watching
- watching brief
- watching-brief
- watch it
- watch-it
- watch-like-a-hawk
- watch list
- watch-list
- watchmaker
- watchmaking
- watchman
- watch out
- watch-out
- watch-out
- watch-out-for
- watch out for sb/sth
- watch-out-for-sb-sth
- watch out for someone/something
- watch-over
- watch over sb