※ 引述《xx52002 (长门有希好萌(′▽‵))》之铭言： : (1)Suppose the function f has the property that │f(x) - f(t)│≦│x-t│ : for each pair of points x,t in the interval (a,b). : Prove that f is continuous on (a,b) : (2)Given that f and g are continuous functions on [a,b], and the f(a)>g(a) : and g(b)>f(b), show that there exists at least one number c 属於 (a,b) : such that f(c) = g(c) : 拜托各位了 QQ (1) 令 h→0　such that ｜f(x+h)－f(x)｜≦｜(x+h)－x｜＝｜h｜　(移项可得) ｜ f(x+h)－f(x) ｜ => ｜lim ______________｜ ≦ １ => ｜f'(x)｜≦ 1 ∴ f'(x) 於(a,b)存在 ｜h->0 　　h ｜ 　 f(x)－f(t) 　∴　lim f(x) ＝ lim｛〔 ____________ × (x－t)〕＋ f(t)｝＝f'(x)× 0 ＋f(t) x->t x->t x－t ＝ f(t) 极限存在 for t in (a,b)　　∴ f 连续 on (a,b) --

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