-
Notifications
You must be signed in to change notification settings - Fork 0
/
tmp.html
42 lines (42 loc) · 7.35 KB
/
tmp.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
<!DOCTYPE html><html><head><meta charset="UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"><meta name="description" content=""><meta name="keywords" content=""><meta name="author" content="sherco,undefined"><meta name="copyright" content="sherco"><title>loser's monologue | sherco's home</title><link rel="shortcut icon" href="/my-favicon.ico"><link rel="stylesheet" href="/css/index.css?version=1.5.6"><link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/css/font-awesome.min.css?version=1.5.6"><link rel="dns-prefetch" href="https://cdn.staticfile.org"><link rel="dns-prefetch" href="https://cdn.bootcss.com"><link rel="dns-prefetch" href="https://creativecommons.org"><link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/npm/gitalk/dist/gitalk.min.css"><script src="https://cdn.jsdelivr.net/gh/upupming/gitalk@36368e5dffd049e956cdbbd751ff96c28d8255cf/dist/gitalk.min.js"></script><script src="https://cdn.jsdelivr.net/npm/[email protected]/js/md5.min.js"></script><link rel="dns-prefetch" href="https://hm.baidu.com"><script>var _hmt = _hmt || [];
(function() {
var hm = document.createElement("script");
hm.src = "https://hm.baidu.com/hm.js?xoSwZBAtKJ";
var s = document.getElementsByTagName("script")[0];
s.parentNode.insertBefore(hm, s);
})();</script><script>var GLOBAL_CONFIG = {
root: '/',
algolia: undefined,
localSearch: undefined,
copy: {
success: 'Copy successfully',
error: 'Copy error',
noSupport: 'The browser does not support'
}
} </script></head><body><canvas class="fireworks"></canvas><i class="fa fa-arrow-right" id="toggle-sidebar" aria-hidden="true"></i><div id="sidebar"><div class="author-info"><div class="author-info__avatar text-center"><img src="https://s1.ax1x.com/2018/07/11/PuD4jx.jpg"></div><div class="author-info__name text-center">sherco</div><div class="author-info__description text-center"></div><hr><div class="author-info-articles"><a class="author-info-articles__archives article-meta" href="/archives"><span class="pull-left">Articles</span><span class="pull-right">1</span></a><a class="author-info-articles__tags article-meta" href="/tags"><span class="pull-left">Tags</span><span class="pull-right">2</span></a></div><hr><div class="author-info-links"><div class="author-info-links__title text-center">dalao们</div><a class="author-info-links__name text-center" href="https://jszyxw.github.io/" target="_blank">jszyxw</a><a class="author-info-links__name text-center" href="https://debug18.com/" target="_blank">__debug</a><a class="author-info-links__name text-center" href="https://fuboat.coding.me/blog/" target="_blank">fuboat</a></div></div></div><nav class="https://s1.ax1x.com/2018/07/11/PuDX8A.jpg" id="nav" style="background-image: url(https://s1.ax1x.com/2018/07/11/PuDX8A.jpg)"><div id="page-header"><span class="pull-left"> <a id="site-name" href="/">sherco's home</a></span><i class="fa fa-bars toggle-menu pull-right" aria-hidden="true"></i><span class="pull-right menus"><a class="site-page" href="/">Home</a><a class="site-page" href="/archives">Archives</a><a class="site-page" href="/tags">Tags</a><a class="site-page" href="/categories">Categories</a></span></div><div id="site-info"><div id="site-title">sherco's home</div><div id="site-sub-title">loser's monologue</div><div id="site-social-icons"> <a class="social-icon" href="https://github.com/shercoo" target="_blank"><i class="fa fa-github"></i></a><a class="social-icon" href="https://weibo.com/5689441604/profile?topnav=1&wvr=6" target="_blank"><i class="fa fa-weibo"></i></a><a class="social-icon" href="https://user.qzone.qq.com/1139352192" target="_blank"><i class="fa fa-qq"></i></a></div></div></nav><div id="content-outer"><div class="layout" id="content-inner"><article id="page"><h1></h1><div class="article-container"><a id="more"></a>
<p>真的没什么写的但是要装作作者很勤奋</p>
<p>###证明$(e^x)^{‘} = e^x$<br>$\Delta y = e^{ x + \Delta x}-e^x = e^x(e^{\Delta x} - 1)$<br>$\lim\limits_ {\Delta x \to 0} \frac{\Delta y}{\Delta x} = \lim\limits_ {\Delta x \to 0} e^x \frac{e^{\Delta x}-1}{\Delta x}$<br>令$t=e^{\Delta x}-1$，<br>则$\lim\limits_ {\Delta x \to 0} \frac{\Delta y}{\Delta x}=\lim\limits_ {t \to 0}{e^x \frac{t}{\ln{(t+1)}}}$<br>$=e^x \lim\limits_ {t \to 0 }\frac{1}{\ln{(t+1)^{\frac{1}{t}}}} = e^x \frac{1}{\ln e} = e^x$</p>
<p>###用微分的方法得到一些函数的近似值<br>假设$y=f(x)$在$x=x_0$处可微，则当$\Delta x \to 0$ 时，可以得到<br>$$f(x_0+\Delta x) = f(x_0)+f^’ (x_0)\Delta x+o(\Delta x)$$<br>$o(\Delta x)$是比$\Delta x$更高阶的无穷小量，这里可以把它忽略不计<br>应用这个操作，即$f(x_0+\Delta x) \approx f(x_0)+f^’ (x_0)\Delta x$,就可以得到<br>$$e^x \approx e^(0+x)=e^0+e^0 x=1+x$$<br>$$\ln (1+x) \approx \ln 1 +\frac{1}{1}x=x$$<br>$$(1+x)^{\alpha} \approx 1^{\alpha}+\alpha · 1^{\alpha-1} x =1+\alpha x$$</p>
</div></article><nav id="pagination"><div class="pagination"></div></nav><div id="gitalk-container"></div><script>var gitalk = new Gitalk({
clientID: '49868a37fd93b91b10b8',
clientSecret: '5401470d3675709bb23bbd1121888a7ce8ddc482',
repo: 'shercoo.github.io',
owner: 'shercoo',
admin: 'shercoo',
id: md5(decodeURI(location.pathname)),
language: ''
})
gitalk.render('gitalk-container')</script></div></div><footer><div class="layout" id="footer"><div class="copyright">©2018 - 2019 By sherco</div><div class="framework-info"><span>Driven - </span><a href="http://hexo.io"><span>Hexo</span></a><span class="footer-separator">|</span><span>Theme - </span><a href="https://github.com/Molunerfinn/hexo-theme-melody"><span>Melody</span></a></div><div class="busuanzi"><script async src="//dn-lbstatics.qbox.me/busuanzi/2.3/busuanzi.pure.mini.js"></script><span id="busuanzi_container_site_uv"><i class="fa fa-user"></i><span id="busuanzi_value_site_uv"></span><span></span></span><span class="footer-separator">|</span><span id="busuanzi_container_site_pv"><i class="fa fa-eye"></i><span id="busuanzi_value_site_pv"></span><span></span></span></div></div></footer><i class="fa fa-arrow-up" id="go-up" aria-hidden="true"></i><script src="/js/third-party/anime.min.js"></script><script src="/js/third-party/jquery.min.js"></script><script src="/js/third-party/jquery.fancybox.min.js"></script><script src="/js/third-party/velocity.min.js"></script><script src="/js/third-party/velocity.ui.min.js"></script><script src="/js/utils.js?version=1.5.6"></script><script src="/js/fancybox.js?version=1.5.6"></script><script src="/js/sidebar.js?version=1.5.6"></script><script src="/js/copy.js?version=1.5.6"></script><script src="/js/fireworks.js?version=1.5.6"></script><script src="/js/transition.js?version=1.5.6"></script><script src="/js/scroll.js?version=1.5.6"></script><script src="/js/head.js?version=1.5.6"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
processEscapes: true,
skipTags: ['script', 'noscript', 'style', 'textarea', 'pre', 'code']
}
});
</script><script type="text/x-mathjax-config">MathJax.Hub.Queue(function() {
var all = MathJax.Hub.getAllJax(), i;
for (i=0; i < all.length; i += 1) {
all[i].SourceElement().parentNode.className += ' has-jax';
}
});
</script><script src="https://cdn.jsdelivr.net/npm/mathjax/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></body></html>