急求解一道英文的實(shí)數(shù)分析證明題,關(guān)于極限和連續(xù)定理的
Let f:D -> R and a be an accumulation point（聚點(diǎn)） of D.Define（下定義） the right-handed limit (右側(cè)極限）of f(x) at a as,lim x -> a+ f(x) = L iff（當(dāng)且僅當(dāng)） for every（對(duì)所有） ε > 0 there exists a（存在一個(gè)） σ > 0 such that f(x) - L的絕對(duì)值 < ε,如果 a < x < a+σ and x屬于D.
Similarly （同樣的）,define the left-handed limit （左側(cè)極限）of f(x) at a as,lim x -> a- f(x) = L iff for every ε > 0 there exists a σ > 0 such that f(x) - L的絕對(duì)值 < ε,whenever a-σ < x < a and x屬于D.
證明 lim x -> a f(x) = L iff lim x -> a+ f(x) = L and lim x -> a- f(x) = L.
翻譯的比較粗略 希望大俠能看懂
現(xiàn)在只需要證 若以知 lim x -> a f(x) = L 求證lim x -> a+ f(x) = L 和 lim x -> a- f(x) = L