“limit from the left and right”的概念、定义、习题解题方法及翻译-数学辞典

单词

limit from the left and right

释义

limit from the left and right

The statement that f(x) tends to l as x tends to a from the left can be written: f(x)→ l as x → a−. Another way of writing this is

The formal definition says that this is so if, given ε>0, there is a number δ>0 such that, for all x strictly between a−δ and a, f(x) lies between l−ε and l + ε. In place of x → a−, some authors use x ↗ a. In the same way, the statement that f(x) tends to l as x tends to a from the right can be written: f(x) → l as x → a +. Another way of writing this is

The formal definition says that this is so if, given ε>0, there is a number δ>0 such that, for all x strictly between a and a + δ, f(x) lies between l−ε and l + ε. In place of x → a +, some authors use x ↘ a. For example, if f(x) = x−[x], then

The graph of x – [x]

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