一、题目![题目 - 荒原之梦](https://documents.zhaokaifeng.com/uploads/2017/06/06/f68a9e590526998388b0f9b71bd5d3f73dda4ed9764819fe8f36488fa537e9b9499f465fd201d7c117b8901c3ad071915a34a688058a739ebc39835753a8d7cc.svg)
设可导函数 $f(x)>0$, 则:
$$
\lim \limits_{n \rightarrow \infty} n \ln \frac{f\left(\frac{1}{n}\right)}{f(0)} = ?
$$
难度评级:
二、解析 ![解析 - 荒原之梦](https://documents.zhaokaifeng.com/uploads/2017/06/06/6fff698aa5c66c6c7a143e3d2a00fa8ee7eab76be5360d89eb43a03143848e8cd60377c76bf830c93ec6603be5af661d9c52238834792ea548bf14de10b05ad9.svg)
首先:
$$
\lim \limits_{n \rightarrow \infty} n \textcolor{orangered}{\ln \frac{f\left(\frac{1}{n}\right)}{f(0)} } =
$$
$$
\lim \limits_{n \rightarrow \infty} n \textcolor{orangered}{\left[ \ln f\left(\frac{1}{n}\right) – \ln f(0) \right] } =
$$
$$
\lim \limits_{n \rightarrow \infty} \frac{\ln f\left(\frac{1}{n}\right) – \ln f(0)}{\frac{1}{n} – 0} =
$$
$$
\lim \limits_{x \rightarrow 0} \frac{\ln f\left( x \right) – \ln f(0)}{x – 0} =
$$
$$
\lim \limits_{x \rightarrow 0} \left[ \ln f(x) \right]^{\prime} =
$$
$$
\lim \limits_{x \rightarrow 0} \frac{f^{\prime}(x)}{f(x)} = \textcolor{springgreen}{ \frac{f^{\prime}(0)}{f(0)} }
$$
高等数学![箭头 - 荒原之梦](https://documents.zhaokaifeng.com/uploads/2017/06/06/c19692009799eac2a7eb5b9d73167ae3dd6cad169ea3ccdbeb97491b80e87593cfa7384844ec1720d0fb9cf5f00ac456f249d047b61ce2d90bdd241e042f4d89.svg)
涵盖高等数学基础概念、解题技巧等内容,图文并茂,计算过程清晰严谨。
线性代数![箭头 - 荒原之梦](https://documents.zhaokaifeng.com/uploads/2017/06/06/c19692009799eac2a7eb5b9d73167ae3dd6cad169ea3ccdbeb97491b80e87593cfa7384844ec1720d0fb9cf5f00ac456f249d047b61ce2d90bdd241e042f4d89.svg)
以独特的视角解析线性代数,让繁复的知识变得直观明了。
特别专题![箭头 - 荒原之梦](https://documents.zhaokaifeng.com/uploads/2017/06/06/c19692009799eac2a7eb5b9d73167ae3dd6cad169ea3ccdbeb97491b80e87593cfa7384844ec1720d0fb9cf5f00ac456f249d047b61ce2d90bdd241e042f4d89.svg)
通过专题的形式对数学知识结构做必要的补充,使所学知识更加连贯坚实。