英语词汇“mean-value theorem”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

mean-value theorem n. Mathematics an elementary theorem in mathematical analysis, which states that if a real function f(x) is continuous on the closed interval a ≦ x ≦ b and differentiable on the open interval a < x < b, then there is a point in the open interval at which the first derivative of the function is equal to ^{f(b) − f(a)}/ _{b − a}; (also) any of several generalizations of this theorem.

ΚΠ

1900 Trans. Amer. Math. Soc. 1 504 Applying the usual mean value theorem, we have J_ν = C_νΔ(z)dz.

1957 T. M. Apostol Math. Anal. v. 93 One of the most useful tools of differential calculus is the Mean Value Theorem... There is at least one interior point x₀ of (a, b) such that f(b) − f(a) = f′(x₀)(b − a).

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xix. 411 If in the mean value theorem the values f(a) and f(b) are equal then..there exists in this interval a tangent parallel to the x-axis.

1990 H. A. Priestley Introd. Complex Anal. (rev. ed.) 194 The Mean-value theorem does not extend to holomorphic functions.

单词	mean-value theorem
释义	> as lemmas mean-value theorem mean-value theorem n. Mathematics an elementary theorem in mathematical analysis, which states that if a real function f(x) is continuous on the closed interval a ≦ x ≦ b and differentiable on the open interval a < x < b, then there is a point in the open interval at which the first derivative of the function is equal to ^{f(b) − f(a)}/ _{b − a}; (also) any of several generalizations of this theorem. ΚΠ 1900 Trans. Amer. Math. Soc. 1 504 Applying the usual mean value theorem, we have J_ν = C_νΔ(z)dz. 1957 T. M. Apostol Math. Anal. v. 93 One of the most useful tools of differential calculus is the Mean Value Theorem... There is at least one interior point x₀ of (a, b) such that f(b) − f(a) = f′(x₀)(b − a). 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xix. 411 If in the mean value theorem the values f(a) and f(b) are equal then..there exists in this interval a tangent parallel to the x-axis. 1990 H. A. Priestley Introd. Complex Anal. (rev. ed.) 194 The Mean-value theorem does not extend to holomorphic functions. extracted from meanadj.² < as lemmas
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