# Quod Erat Demonstrandum

## 2011/03/31

### To 6C students

Filed under: Pure Mathematics — johnmayhk @ 5:23 上午

Just a sketch of the solutions to 1-mark questions in the previous quiz.

Q.7

Denote [$x$] as the greatest integer not greater than $x$.

Does $\displaystyle \lim_{x\rightarrow 0-}(\frac{x}{2011}[\frac{2012}{x}]-\frac{2011}{x}[\frac{x}{2012}])$ exist?

Hint: (more…)

## 2011/03/30

### M2 三點

Filed under: NSS,Pure Mathematics — johnmayhk @ 4:17 下午
Tags:

1.

Evaluate $\int_{0}^{y} \ln(1+\tan x \tan y)dx$.

### [FW][TED]Marcus du Sautoy: Symmetry, reality’s riddle

Filed under: Fun,University Mathematics — johnmayhk @ 5:41 上午

## 2011/03/29

### 某古算題

Filed under: Junior Form Mathematics — johnmayhk @ 2:43 下午

「今有共買璡（石之似玉者《說文》），人出半（即 $\frac{1}{2}$），盈四；人出少半（即 $\frac{1}{3}$），不足三。問璡價。」

Solution
Let $n$ be the number of buyers.
$\frac{n}{2}-4=\frac{n}{3}+3\Rightarrow n=42$
Hence the price is $\frac{42}{2}-4=17$.

## 2011/03/24

### use series instead of lhopital

Filed under: Additional / Applied Mathematics,HKALE,Pure Mathematics — johnmayhk @ 3:10 下午

$\displaystyle \lim_{x\rightarrow 0}(\frac{\sin^{-1}x}{x})^{\frac{1}{x^2}}$

## 2011/03/20

### [FW][song] Mandelbrot Set

Filed under: Fun,mathematics — johnmayhk @ 4:38 下午

## 2011/03/18

### 某兩題中四數

Filed under: NSS — johnmayhk @ 5:02 下午

1.

A wire of 80 cm long is cut into two pieces and each wire is bent into a square.
The length of each side of the smaller square is $x$ cm.

(a) Express the total area of the two squares in terms of $x$.
(b) Find the minimum area of the two squares in total.

## 2011/03/17

### 某有關開方根的題目

Filed under: Junior Form Mathematics — johnmayhk @ 3:44 下午
Tags:

$(a+b)+(c+d)=(a+c)+(b+d)$

$(\sqrt{a}+\sqrt{b})+(\sqrt{c}+\sqrt{d})=(\sqrt{a}+\sqrt{c})+(\sqrt{b}+\sqrt{d})$

## 2011/03/15

### 混疊圖像

Filed under: Fun — johnmayhk @ 12:34 下午

《題西林壁》
（宋）蘇軾

## 2011/03/10

### 金比銀比銅比

Filed under: Junior Form Mathematics — johnmayhk @ 3:27 下午

## 2011/03/09

Filed under: Fun — johnmayhk @ 8:51 下午

Easy but fun.

## 2011/03/08

Filed under: Physics,University Mathematics — johnmayhk @ 5:27 下午

## 2011/03/04

### [FW] An evolving landscape of a 3D fractal surface

Filed under: Fun — johnmayhk @ 3:45 下午

## 2011/03/03

### Polynomial identity

Is the following an identity? Prove or disprove your claim:

$(x+1)(x-3)+1=(x+2)(x-1)$

This is a trivial (more…)

## 2011/03/02

### 當 x 接近零，(1+1/x)^x 如何？

Filed under: Pure Mathematics — johnmayhk @ 5:07 下午
Tags:

$\displaystyle \lim_{x\rightarrow \infty}(1+\frac{1}{x})^{x} = e$

$\displaystyle \lim_{x\rightarrow \infty}(2+\frac{1}{x})^{x} = ?$

$\displaystyle \lim_{x\rightarrow 0}(1+\frac{1}{x})^{x} = ?$