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設|f’(x)|≤M 則,對任意x,y∈I根據拉格朗日中值定理,有|f(y)–f(x)|≤M|y-x| 於是,對任給ε>0,取δ=ε/ M,則當|y-x|<δ時就有|f(y)–f(x)|≤M|y-x|<M(ε/ M)=ε ∴命題得證,證畢
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