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Last Update: 10/05/2024 09:24 AM
Current Deck: 25考研高等数学公式+概念+定理+典例【5.0版】【数二版】【latex精制版】::02函数，极限，连续::02极限::06求极限的基本方法::06利用夹逼准则求极限
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问题
夹逼准则求极限表格
答案
\(\text{夹逼准则}\begin{cases}
\text{定义}:\text{若存在}N,\text{当}n>N\text{时},x_n\leqslant y_n\leqslant z_n\text{且}\underset{n\rightarrow \infty}{\lim}x_n=\underset{n\rightarrow \infty}{\lim}z_n=a,\text{则}\underset{n\rightarrow \infty}{\lim}y_n=a\\
\text{求极限放缩}\begin{cases}
\text{无限项相加}:n\cdot U_{\min}\leqslant \displaystyle\sum_{i=1}^n{U_i}\leqslant n\cdot U_{\max}\langle \text{大小都要找},\text{齐次不动}\rangle\\
\text{有限项相加}:1\cdot U_{\max }\leqslant \displaystyle\sum_{i=1}^n{U_i}\leqslant n\cdot U_{\max}({U_i}>0)\\
\text{若干项乘积略去小于}1\text{的因子},\text{则放大},\text{略去大于}1\text{的因子},\text{则缩小}\\
\end{cases}\\
\end{cases}\)
\text{定义}:\text{若存在}N,\text{当}n>N\text{时},x_n\leqslant y_n\leqslant z_n\text{且}\underset{n\rightarrow \infty}{\lim}x_n=\underset{n\rightarrow \infty}{\lim}z_n=a,\text{则}\underset{n\rightarrow \infty}{\lim}y_n=a\\
\text{求极限放缩}\begin{cases}
\text{无限项相加}:n\cdot U_{\min}\leqslant \displaystyle\sum_{i=1}^n{U_i}\leqslant n\cdot U_{\max}\langle \text{大小都要找},\text{齐次不动}\rangle\\
\text{有限项相加}:1\cdot U_{\max }\leqslant \displaystyle\sum_{i=1}^n{U_i}\leqslant n\cdot U_{\max}({U_i}>0)\\
\text{若干项乘积略去小于}1\text{的因子},\text{则放大},\text{略去大于}1\text{的因子},\text{则缩小}\\
\end{cases}\\
\end{cases}\)
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