Notes in 04利用洛必达求极限

To Subscribe, use this Key

Status	Last Update	Fields
Published	10/05/2024	利用洛必达法则求极限 未定式条件结论\(\frac{0}{0}\text{型}\)\(\text { 设(1) } \displaystyle\lim _{x \rightarrow a} f(x)=0 \text { 且 } \displaystyle\lim _{x \rightarr…
Published	10/05/2024	1.\(f(x)\)在点\(a\)处连续，能对 \(\begin{align} \lim _{x \rightarrow a} \frac{f(x)}{g(x)} \end{align}\) 使用洛必达法则吗.
Published	10/05/2024	2.\(f(x)\)在\(a\)点导数存在，能对 \(\begin{align} \lim _{x \rightarrow a} \frac{f(x)}{g(x)} \end{align}\) 使用洛必达法则吗.
Published	10/05/2024	3.\(f(x)\)在a处二阶可导,能对 \(\begin{align} \displaystyle\lim _{x \rightarrow a} \frac{f(x)}{g(x)} \end{align}\) 使用两次洛必达法则吗.
Published	10/05/2024	4.在 \(x \rightarrow 0\) 时, 极限式子中含有 \(\sin \frac{1}{x}, \cos \frac{1}{x}\); 或在 \(x \rightarrow \infty\) 时, 极限式子中含有 \(\sin x\), \(\cos x\).请问这样的极限式子可以用洛…
Published	10/05/2024	5.如果对极限分子、分母分别求导后的极限不存在或不为 \(\infty\), 请问此极限还用洛必达法则吗, 是否意味着原极限不存在.
Published	10/05/2024	6.有些极限若用洛必达法则来求, 将产生循环现象而永远求不出原极限.\(\underset{x \rightarrow+\infty}{\lim} \frac{\mathrm{e}^{x}+\cos x}{\mathrm{e}^{x}+\sin x}\left(\frac{\infty}{…
Published	10/05/2024	7.数列极限可以直接用洛必达呢
Published	10/05/2024	8.\(\text{推广的洛必达法则}\left( \frac{*}{\infty}\text{型} \right) \)(了解)\(\text{设}\left( 1 \right) \underset{x\rightarrow a}{\lim}F\left( x \right) =\infty ,…
Status	Last Update	Fields