“limit from the left and right”的概念、定义、翻译、参考文献-科学参考

limit from the left and right

Mathematics

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

$lim_{x \to a^{−}} f (x) = l .$

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

$lim_{x \to a^{+}} f (x) = l .$

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

$lim_{x \to 1^{-}} f (x) = 1, lim_{x \to 1^{+}} f (x) = 0.$

The graph of x – [x]

单词	limit from the left and right
释义	limit from the left and right Mathematics 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 $lim_{x \to a^{−}} f (x) = l .$ 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 $lim_{x \to a^{+}} f (x) = l .$ 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 $lim_{x \to 1^{-}} f (x) = 1, lim_{x \to 1^{+}} f (x) = 0.$ The graph of x – [x]
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