# Quod Erat Demonstrandum

## 2011/08/09

### Past papers 1964, 1971

Filed under: Additional / Applied Mathematics,Fun,HKALE,Pure Mathematics — johnmayhk @ 11:38 上午

Matriculation Examination (1964)

Pure Mathematics I,II
Applied Mathematics I,II  (more…)

## 2011/04/15

### 又談MVT

Filed under: Fun,HKALE,Pure Mathematics — johnmayhk @ 11:05 下午
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## 2011/04/13

### 解微分方程

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 8:50 上午

[Hardsell 廣告腔] 解微分方程？用

http://www.wolframalpha.com/

y"+y=sin(x) (more…)

## 2011/03/24

### use series instead of lhopital

Filed under: Additional / Applied Mathematics,HKALE,Pure Mathematics — johnmayhk @ 3:10 下午 $\displaystyle \lim_{x\rightarrow 0}(\frac{\sin^{-1}x}{x})^{\frac{1}{x^2}}$

## 2011/01/07

### Exercise in counting balls and boxes

Filed under: Additional / Applied Mathematics,HKALE,NSS — johnmayhk @ 7:43 上午
Tags:

The following is just a basic counting exercise from a secondary mathematics textbook (used in Taiwan, I guess), enjoy.

Find the number of ways of (more…)

## 2010/11/20

### 唔打：唯一解與delta非零

Filed under: HKALE,NSS,Pure Mathematics — johnmayhk @ 5:56 下午

## 2010/11/10

### 有解條件

Filed under: HKALE,Pure Mathematics — johnmayhk @ 3:10 下午 $p,q$ 為常數，問在什麼條件下 $px = q$ 有解？ (more…)

## 2010/10/27

### 玩玩系列：二次方程

Filed under: HKALE,NSS,Pure Mathematics — johnmayhk @ 10:11 上午

1. 設 $a,b,c$ 是奇數（odd numbers），證明 $ax^2 + bx + c = 0$ 無整數根（integral root）。
2. 已知 $e$ $\pi$ 是超越數，證明 $e + \pi$ $e\pi$ 兩者中起碼一個是超越數。

## 2010/10/18

### 某插值法習題

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 2:56 下午
Tags: $f(x) = \sin(\frac{\pi}{2}x)$

## 2010/09/27

### series by wolfram alpha

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 5:40 下午

Expand $\sin^{-1}x$ about $x = 0$.

http://www.wolframalpha.com/

## 2010/07/26

### MVT 某推廣

Filed under: HKALE,Pure Mathematics — johnmayhk @ 11:54 上午
Tags: , $F(x) = -3x + \frac{\pi}{2}\cos(\frac{\pi}{2}x) + \frac{e^x}{e - 1} + \frac{1}{(x + 2)\ln 2}$ 在區間 (0,1) 存在零點 ………. (*) $F(0) , F(1)$ 皆大於零，故不宜用介值定理（Intermediate Value Theorem）。

## 2010/07/22

### 暑期無聊閱讀

Filed under: Additional / Applied Mathematics,HKALE,HKCEE — johnmayhk @ 9:02 上午
Tags:

If you worked for a mining company the following might be a typical problem: There are two intersecting mine shafts that meet at an angle of 123 $^o$, as shown in the figure above. The straight shaft has a width of 7 feet, while the entrance shaft is 9 feet wide. What is the longest ladder that can be negotiate the turn? You can neglect the thickness of the ladder members, and assume it is not tipped as it is maneuvered around the corner. Your solution should provide for the general case in which the angle, A, is a variable, as well as the widths of the shafts. (more…)

## 2010/06/17

### 重複數算一例

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 11:05 上午
Tags: http://www.hkms-nss.net/discuz/home/space.php?uid=423&do=blog&id=38

## 2010/06/16

### 單增區域

Filed under: HKALE,Pure Mathematics — johnmayhk @ 12:37 上午
Tags: ,  $f'(a) > 0$

（見圖）

## 2010/06/01

### Just a revision on counting

Filed under: Additional / Applied Mathematics,HKALE,Teaching — johnmayhk @ 4:03 下午
Tags:

Here is just an ordinary question:

“An elevator starts carrying five persons at the ground floor and then goes up. It can stop at any floor of the building (from the first floor to the third floor). Events that people leaving the elevator are assumed to be independent. Let X be the number of ‘stop’ of the elevator during a “going-up” journey. Find the value of E(X)."

We may use “balls and boxes" (more…)

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