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Cauchy's Mean-Value Theorem (The Generalized Mean-Value Theorem) 設f(x)、g(x)在[a,b]連續，在(a,b)可微分，則存在一個c€(a,b)使得f'(c)[ g(b) ... ... <看更多>

Mean Value Theorem ... 證明：. (a) 方程x3 − 3x + c = 0(c ∈ R)在區間[0, 1]內不可能有兩個不同的實 ... 應用Lagrange中值定理證明下列不等式：. ... <看更多>

Proof of the Intermediate Value Theorem ... Theorem: Let f be continuous on [a,b] and assume f(a)<f(b). Then for every k such that f(a)<k<f(b), there exists a c∈ ... ... <看更多>