mean value theorem वाक्य
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- *PM : Proof of Bernoulli's Inequality employing the Mean Value Theorem, id = 7803 new !-- WP guess : Proof of Bernoulli's Inequality employing the Mean Value Theorem-- Status:
- This name is justified by the mean value theorem, which states that for a differentiable function " f ", its derivative " f2 " reaches its mean value at some point in the interval.
- If is another such collection of solutions, one can show ( using some linear algebra and the mean value theorem ) that this has the same family of level sets but with a possibly different choice of constants for each set.
- Jean Dieudonn?in his classic treatise " Foundations of Modern Analysis " discards the mean value theorem and replaces it by mean inequality as the proof is not constructive and one cannot find the mean value and in applications one only needs mean inequality.
- Therefore, " V " has to be constant on " I ", because otherwise we would obtain a contradiction to the mean value theorem ( applied separately to the real and imaginary part in the complex-valued case ).
- If a real-valued, differentiable function " f ", defined on an interval " I " of the real line, has zero derivative everywhere, then it is constant, as an application of the mean value theorem shows.
- But the requirements for " f " needed for the use of mean value theorem are too strong, if one aims to prove the claim in the case that " f " ( " k " ) is only absolutely continuous.
- For example, if the sequence consists of differentiable functions or functions with some regularity ( e . g ., the functions are solutions of a differential equation ), then the mean value theorem or some other kinds of estimates can be used to show the sequence is equicontinuous.
- For what it's worth, it's the mean value theorem for integrals ( which some might say is " more fundamental " than the fundamental theorem & mdash; it is at least more intuitive ) . talk ) 12 : 13, 20 April 2012 ( UTC)
- Parameshvara ( c . 1370 1460 ) wrote commentaries on the works of Bhaskara I, Aryabhata and Bhaskara II . His " Lilavati Bhasya ", a commentary on Bhaskara II's " Lilavati ", contains one of his important discoveries : a version of the mean value theorem.
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