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Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Theorem: $$c, d\in {\bf R}, \lim_{x\rightarrow \infty} f(x)=c>0, \lim_{x\rightarrow \infty} g(x) =d>0$$ then $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$ Proof: Because $y(x)=ln(x)$ is c

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Let hexo support mathjax

UpdateThe original answer fails on some mathjax expressions. So don’t use it. Currently changing marked.js works for me. Just use the method below. It works for me. First introduce mathjax into our bl

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Proof of the limit's composition law when x approaches infinity

Theorem: If $f(x)$ is continous at $b$ and $\lim\limits_{x \to\infty}g(x) = b$, then $$\lim\limits_{x \to \infty}f(g(x)) = f(b) = f(\lim\limits_{x\to \infty}g(x))\tag1$$ Proof: Because $f(x)$ is con

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Calculate $$\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$$

I came upon the calculation of $\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$ when I was reviewing Poisson distribution. Notice that $\lambda_n = np_n(n\in\mathbb{Z}_{\geq 0}, 0\leq p \leq 1)$ and

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Hexo Source Code Demystified

PrefaceHexo is an excellent static blog generator, I read its source code recently, and I think it’s worth sharing the inner mechanism of its source code. GeneratorWhen you run the command hexo genera

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The fee paid to freelancer is not refundable

About two days ago, I got a message from my phone that I was charged for ￥110.72. The money was taken directly from my debit card. At first, I thought the money was stolen using some high-end technolo

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I finished reading "The catcher in the rhy"

I finished reading “The catcher in the rhy” yesterday. I don’t think this is an excellent book. The main character in this book just hates everything. I have no idea why he thinks in this way, though

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install flash plugin in firefox on arch linux

First, install flashplugin. 1sudo pacman -S flashplugin Then if you launch firefox, you will find out that there’s no sound when playing flash in it. Launch it from the terminal, you will find out the

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connect to wifi via commandline on arch

I just spent hours connecting to the wireless network on archlinux today. Finally I resorted to various tools in commandline. Here’s how I do it. Make sure you run the following commands as root to av

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It's pretty hard to concentrate these days

Honestly I feel awful these days, it goes the same for yesterday. I created a task that I needed to code for at least three hours for my project every day, but while I was anxious, it was really hard