https://www.zhuzhugst.com/ 2026-07-25T19:18:51+00:00 https://www.zhuzhugst.com/ https://www.zhuzhugst.com/lib/exe/fetch.php?media=logo.png text/html 2026-07-20T05:34:14+00:00 张叶安 (midas@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?id=%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90:1_%E5%9E%8B%E6%9C%AA%E5%AE%9A%E5%BC%8F&rev=1784525654&do=diff 1^∞ 型未定式详解 一、什么是 1^∞ 型？ 当求极限时，如果底数趋向于 1，而指数趋向于 ∞，则形如： $$\lim u(x)^{v(x)}$$ 其中 $u(x) \to 1$，$v(x) \to \infty$，这种形式称为 1^∞ 型未定式。 " 注意：这里的 “1” 不是真正的常数 1，而是$1^\infty$$e^a$$1^2$$1^{100}$$(1+\frac{1}{n})^n$$n \to \infty$$(1+\frac{2}{n})^n$$n \to \infty$$(1-\frac{1}{n})^n$$n \to \infty$$1^\infty = 1$$1^\infty$$y = u(x)^{v(x)}$$$\ln y = v(x) \cdot \ln u(x)$$$u \to 1$$\ln u = \ln(1 + (u-1)) \sim u - 1$$$\lim \ln y = \lim v(x) \cdot (u(x) - 1)$$$$\lim y = e^{\lim v(x) \cdot (u(x) - 1)}$$$$\boxed{\lim… text/html 2026-04-23T14:51:19+00:00 张叶安 (midas@undisclosed.example.com) https://www.zhuzhugst.com/doku.php?image=%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90%3Ahistory_of_the_method_of_fluxions_normalized_.pdf&ns=%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90&rev=1776955879&tab_details=history&media_do=diff&do=media <img src="https://www.zhuzhugst.com/lib/images/fileicons/svg/pdf.svg" alt="history_of_the_method_of_fluxions_normalized_.pdf" loading="lazy" width="500" height="500" />