An ESL Learner

"星期二檔案：公平貿易，良心消費者" / "杯中的貧與富" 的片尾曲叫做什麼？

萬分感激 ！！！

The pushers are unlicensed dealers in illegal drugs. The "pushers who are less bound by civil law than are the police who oppose them" are one of the reasons for drug abuse.

The phrase is not a complete sentence. The pushers are not the police.

Does the phrase imply

1) The pushers are less bound by the civil law than by the police, or

2) The pushers are less bound by the civil law than the police, or

3) Anything else?

THX!

The pushers are unlicensed dealers in illegal drugs. The phrase "pushers who are less bound by civil law than are the police who oppose them" states one of the reasons for drug abuse.

Does the phrase mean

1) The pushers are less bound by the civil law than by the police, or

2) The pushers are less bound by the civil law than the police, or

3) Anything else?

THX!

我分別用了三角代入法，以及普通的代入法，去計算 "∫ 3x^3/(x^2 + 1)^3 dx"。兩個答案不同，為什麼？麻煩看看我有無計錯：

三角代入法：

∫ 3x^3/(x^2 + 1)^3 dx

= ∫ 3x^3/(1^2 + x^2)^3 dx

Let x = tanθ. (trigonometric substitution)

dx/dθ = sec^2θ

dx = sec^2θ dθ

= ∫ 3 * tan^3θ/(1 + tan^2θ)^3 * sec^2θ dθ

= ∫ 3 * tan^3θ/sec^6θ * sec^2θ dθ

= ∫ 3 * tan^3θ/sec^4θ dθ

= ∫ 3 * sin^3θcosθ dθ

Let u = sinθ.

du/dθ = cosθ

dθ = du/cosθ

= ∫ 3 * u^3 du

= 3/4 * u^4 + C

= 3/4 * sin^4θ + C

= 3/4 * (x/√(1 + x^2))^4 + C

= 3/4 * x^4/(1 + x^2)^2 + C

普通的代入法：

∫ 3x^3/(x^2 + 1)^3 dx

Let u = x^2 + 1.

du/dx = 2x

dx = du/2x

= ∫ 3x^3/u^3 du/2x

= ∫ 3/2 * x^2/u^3 du

= ∫ 3/2 * (u - 1)/u^3 du

(u - 1)/u^3 = A/u + B/u^2 + C/u^3 (partial fraction)

u - 1 = Au^2 + Bu + C

A = 0

B = 1

C = -1

= 3/2 * ∫ 1/u^2 - 1/u^3 du

= 3/2 * (-1 * 1/u - 1/(-2) * 1/u^2) + C

= 3/2 * (1/2 * 1/u^2 - 1/u) + C

= 3/2 * (1/(2u^2) - 2u/(2u^2)) + C

= 3/2 * (1 - 2u)/(2u^2) + C

= 3/4 * (1 - 2u)/u^2 + C

= 3/4 * (1 - 2(x^2 + 1))/(x^2 + 1)^2 + C

= 3/4 * (-2x^2 - 1)/(x^2 + 1)^2 + C

= -3/4 * (2x^2 + 1)/(x^2 + 1)^2 + C

If f(x) ≡ f(a - x), prove 2 * ∫(from 0 to a) x * f(x) dx = a * ∫(from 0 to a) f(x) dx.

Could you mention what properties of the definite integral you used?

THX!

(等比數列) 王小姐參加了一個為期十年的投資計劃，每年的第一天她都會存入一筆款項。她第一年把 $12000 存入戶口。從第二年開始，她每年存入戶口的款項都比前一年的多 5%。

b) 如果該計劃每年有 8% 的回報，求第 11 年開始時她可獲得的本利和。

答案是 $229000，我求不到。

THX

假設 P，P ⇒ Q 及 Q ⇒ R，但同時 ~R。那麼我們除了求出 ~P 外，還可不可以求出 ~Q 呢？

What does this sentence mean: "Be it a school project or an assignment students are exploring the world through Internet."

You may refer to http://voices.yahoo.com/internet-its-effect-educat... .

THX!

http://en.wiktionary.org/wiki/inflate

There is a sentence in the right-hand corner: Girl inflating a red balloon by blowing into it.

Why there isn't an "a" before the word "girl" in that sentence?

THX!

若

x + z = 0

-y + z = 1

3x + y + 2z = -1

有解 (x, y, z) 滿足 (x - p)^2 + y^2 + z^2 = 1,

求 p 值的範圍。

Although Amazon claimed that there is free 3G, but "You may be charged a fee for wireless connectivity for your use of other wireless services on your Device, such as Web browsing and downloading of personal files".

Will Amazon notice me to be charged when I use 3G with my Kindle in places outside the US (e.g. Hong Kong)?

THX!

I don't understand what it means: "... but not so different that it is difficult to learn from."

Can anybody read this book review ( i.e. http://www.readability.com/articles/iyvesoqd ) and explain?

THX!

一 6 位正整數，由 2 個不同的非零數字組成，分別佔 2 個及 4 個位，共有多少個可能？

THX!

"The design makes the dress beautiful."

Is this sentence grammatically correct?

The default button is shutdown button, but I want to change it into sleep button. How?

I use Windows 7.

THX!

The default button is shutdown button, but I want to change it into sleep button. How?

I use Windows 7.

THX!

What does "He was so foolish as to lie." mean???

THX!

求曲線 C: x^2 + 2y^2 = 36 通過 (1,0) 的法線方程。

我想知道如何用代數方法解。

THX!

Find the equations of the normal lines to the graph of x^2 + 2y^2 = 36 that pass through point (1,0).

I found one, that is y = 0, but the book says y = 4x - 4 and y = -4x + 4 are answers too. I can't find the other two. How do you solve this question?

THX!

A farmer who studied economics said, "Under a competitive market, the price of each apple must be the same as the marginal cost for each apple. Thus, there is no difference between the price and marginal cost, and the amount I can receive is exactly my cost of production. Thus, a competitive market is not good for farmers." Do you agree? Explain your answer.

THX!