※ 引述《KOREALee (韓國最高)》之銘言：
: Prove that f is continuous at a if and only if
: lim f(a+h) = f(a)
: h→0
Suppose that f is continuous at x = a. Given ε> 0,
there is δ>0 such that |f(a+h)-f(a)|<ε whenever |(a+h)-a|<δ.
For the reverse case, let x = a be a point in the domain of f.
Assume that lim(h->0) f(a+h) = f(a), then given ε>0 there
is δ= h >0 such that |f(x)-f(a)|<ε whenever |x-a|<δ and x in
the domain of f.
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◆ From: 111.251.245.192
※ 編輯: armopen 來自: 111.251.245.192 (01/29 17:08)