屋企真係一個寶庫

無喇喇搵到一本關於 ODE ge 書 (學校 textbook 太貴買唔起)，內有 500 多條 solved problem = =，又有 brief review of 相關 material，正好補返我冇上堂聽 ge 不足，睇 powerpoint 真係睇到好攰 (我一直都係電腦睇)。

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今日返學校去拎返份 math 190 功課，TA 語重心長咁俾左一個 comment 我。

在 latex 裏打 $\sum$ 會有 $\sum$，打 $\displaystyle \sum$ 會有 $\displaystyle \sum$，這就是 displaystyle。

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Problem. Let  $f:[0,\infty)\to\mathbb{R}$ with $f(0)=-1$ be a differentiable function so that $|f(x)-f'(x)|<1,\forall x\ge 0$.

a) Prove that $f$ does have a limit that is infinite.
b) Give an example of such a function.

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Problem. Evaluate $\displaystyle\lim_{n\to\infty }n\left(\frac{1^{\alpha }+2^{\alpha }+...+n^{\alpha }}{n^{\alpha+1 }}-\frac{1}{\alpha+1 }\right)$, $\alpha > 1$.