Notes in 02极限的性质

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Published	10/05/2024	尝试描述函数极限的局部有界性若极限 \(\underset{x \rightarrow x_{0}} {\lim}f(x)\) 存在, 则 \(f(x)\) 在点 \(x_{0}\) ________.
Published	10/05/2024	数列极限的有界性设 \(\underset{n \rightarrow \infty}{\lim} a_{n}\) 存在, 则数列 \(\left\{a_{n}\right\}\) 有界吗; 反之, 结论是否成立？尝试写出证明
Published	10/05/2024	保号性1设 \(\underset{x \rightarrow x_{0}}{\lim} f(x)=A\), 则若 \(A>0\) (或 \(A<0) \Rightarrow \text{______}\).
Published	10/05/2024	保号性2设 \(\underset{x \rightarrow x_{0}}{\lim} f(x)=A\), 则\(\text {若 } x\in \mathring{U}\left( x_0,\delta \right) \text { 时, } f(x) \geqslant 0(\text { …
Published	10/05/2024	保序性1设 \(\underset{x \rightarrow x_{0}} {\lim}f(x)=A, \underset{x \rightarrow x_{0}} {\lim}g(x)=B\), 则若 \(A>B \Rightarrow \exists \delta>0\), 当\(…
Published	10/05/2024	保序性2设 \(\underset{x \rightarrow x_{0}} {\lim}f(x)=A, \underset{x \rightarrow x_{0}} {\lim}g(x)=B\), 则若 \(\exists \delta>0\), 当\(x\in \mathring{U}\l…
Published	10/05/2024	尝试描述极限与无穷小之间的关系\(\lim f(x)=A \Leftrightarrow \text{______} \text {, 其中 } \lim \alpha(x)=0 \text {. }\)
Published	10/05/2024	在自变量的同一变化过程 \(x \rightarrow x_{0}(\) 或 \(x \rightarrow \infty)\) 中, 函数 \(f(x)\) 具有极限 \(A\) 的充分必要条件是________.
Published	10/05/2024	若列极限存在, 则该列的任意子列存在相同的极限吗【汤家凤高数讲义】
Published	10/05/2024	若某一子列极限存在, 则该列极限存在吗【汤家凤高数讲义】
Published	10/05/2024	\( \text { 如果数列 }\left\{x_{n}\right\} \text { 收敛，那么它的极限唯一吗. }\)【同济7版教材】
Published	10/05/2024	极限性质思维导图
Published	10/05/2024	函数极限的唯一性
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