The proof in the text assumes that is increasing. To prove it for all continuous functions,
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The proof in the text assumes that ƒ is increasing. To prove it for all continuous functions, let m(h) and M(h) denote the minimum and maximum of ƒ on [x, x + h] (Figure 15). The continuity of ƒ implies that M(h) = ƒ(x). Show that for h > 0,
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lim m(h)= lim M(h) = f(x). h→0 h→0
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Let f be continuous on a b For h 0 let mh and Mh d...View the full answer
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