See mean value theorem in All languages combined, or Wiktionary
Download JSON data for mean value theorem meaning in English (7.7kB)
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"ref": "1964, J. H. Bramble, L. E. Payne, Some Mean Value Theorems in Electrostatics: Journal of the Society for Industrial and Applied Mathematics, volume 12, page 105",
"text": "Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].",
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"text": "1984 [Nauka, Moscow], Sergey Ermakov, V. V. Nekrutkin (authors and translators), A. S. Sipin (author), Random Processes for Classical Equations of Mathematical Physics, [1984, С. М. Ермаков, В. В. Некруткин, А. С. Сипин, Случайные процессы для решения классических уравнений математической физики], 1989, Kluwer, Softcover Reprint, page xiii,\nFor parabolic equations (Section 5.1) and for the exterior Dirichlet problem (Section 5.2), it is possible to apply the well known mean value theorems."
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"ref": "1994, Patrick W. Thompson, “Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus”, in Paul Cobb, editor, Learning Mathematics, Kluwer, page 167",
"text": "However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.",
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"ref": "2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259",
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"ref": "1990, A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, page 51, In order to get a true bound for the range we may replace the Taylor series in (2) by the mean value theorem, which tells us that f(̃x)=f(̌x)+f'(ζ)(̃x-̌x)",
"text": "for some ζ on the line segment between ̃x and ̌x."
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"ref": "2003, Sylvain Raynes, Ann Rutledge, The Analysis of Structured Securities, Oxford University Press, page 397",
"text": "In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.",
"type": "quotation"
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"ref": "2007, Denise Szecsei, Calculus, The Career Press, page 10",
"text": "The main existence theorems in calculus are the Intermediate Value Theorem, the Extreme Value Theorem, Rolle's Theorem, and the Mean Value Theorem.",
"type": "quotation"
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"The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points."
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"(calculus, uncountable) The theorem that for any real-valued function that is differentiable on an interval, there is a point in that interval where the derivative of the curve equals the slope of the straight line between the graphed function values at the interval's end points."
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"_dis1": "7 93",
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"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"word": "differentiaalilaskennan väliarvolause"
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"word": "teorema del valor medio"
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"text": "Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].",
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"text": "1984 [Nauka, Moscow], Sergey Ermakov, V. V. Nekrutkin (authors and translators), A. S. Sipin (author), Random Processes for Classical Equations of Mathematical Physics, [1984, С. М. Ермаков, В. В. Некруткин, А. С. Сипин, Случайные процессы для решения классических уравнений математической физики], 1989, Kluwer, Softcover Reprint, page xiii,\nFor parabolic equations (Section 5.1) and for the exterior Dirichlet problem (Section 5.2), it is possible to apply the well known mean value theorems."
},
{
"ref": "1994, Patrick W. Thompson, “Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus”, in Paul Cobb, editor, Learning Mathematics, Kluwer, page 167",
"text": "However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.",
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"ref": "2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259",
"text": "We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.",
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},
{
"ref": "2013, Peter D. Lax, Maria Shea Terrell, Calculus With Applications, Springer, page 171",
"text": "The mean value theorem for derivatives provides an important link between the derivative of f on an interval and the behavior of f over the interval.",
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"ref": "1990, A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, page 51, In order to get a true bound for the range we may replace the Taylor series in (2) by the mean value theorem, which tells us that f(̃x)=f(̌x)+f'(ζ)(̃x-̌x)",
"text": "for some ζ on the line segment between ̃x and ̌x."
},
{
"ref": "2003, Sylvain Raynes, Ann Rutledge, The Analysis of Structured Securities, Oxford University Press, page 397",
"text": "In what follows, we will use the mean value theorem, another one of Lagrange's many contributions to numerical analysis.",
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{
"ref": "2007, Denise Szecsei, Calculus, The Career Press, page 10",
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"type": "quotation"
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"sense": "theorem that a point exists where the derivative equals the overall slope",
"word": "Lagrange mean value theorem"
},
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"sense": "theorem that a point exists where the derivative equals the overall slope",
"word": "mean value theorem for derivative"
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"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"word": "differentiaalilaskennan väliarvolause"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"word": "väliarvolause"
},
{
"code": "de",
"lang": "German",
"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
"masculine"
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},
{
"code": "he",
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"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
"masculine"
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"word": "משפט הערך הממוצע"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "mishpát lagránzh",
"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
"masculine"
],
"word": "משפט לגראנז'"
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{
"code": "it",
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"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
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"word": "teorema di Lagrange"
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{
"code": "it",
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"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
"masculine"
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"word": "teorema del valor medio"
},
{
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"lang": "Italian",
"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"tags": [
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"sense": "theorem that for a differentiable function on an interval there is a point in the interval where the derivative equals the overall slope",
"word": "hunain ng tamtaming halga"
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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