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1. I hate it when people prounce ln as lawn

http://www.answers.com/Cauchy" [Broken] (scroll down a bit)
2. I hate it when people prounce ln as lawn

Yes. Take a look at http://www.answers.com/topic/galois-theory". You can even click on the sound button to hear how it's pronounced.
3. I hate it when people prounce ln as lawn

Well... Here in Sweden "root of two" implicitly means "square root of two" since square root is the most ordinary root.
4. I hate it when people prounce ln as lawn

Had a prof in math who pronounced it squirt too :biggrin:
5. A Simple intersection

Paragon: Equations of this kind can't be solved exactly, i.e the solutions can't be expressed in elementary functions. You can use a numerical method, such as Newton's Method, to approximate the solution.
6. Pythagorian theorem

Bhaskara's proof Pythagorean Theorem (scroll down)
7. Simplyfying (Indentitied related)

You're on the right path, my friend! x^4 +Ax^3 + 5x^2 + x + 3 = (x^2 +4)(x^2 -x +B) +Cx +D <=> x^4 +Ax^3 + 5x^2 + x + 3 = x^4 - x^3 + Bx^2 + 4x^2 - 4x + 4B +Cx +D <=(cancellation & simplification)=> Ax^3 + 5x^2 + x + 3 = - x^3 + (B+4)x^2 + (C-4)x + 4B + D
8. Find the Values of the constants in the following indentities

That's right. Just take a look at this trivial example: 1 = \frac{1}{2} + \frac{1}{2} = (definition) = 2*\frac{1}{2} = 1
9. Find the Values of the constants in the following indentities

Yes, you seem to believe that x^2\frac{A}{x^2} = \frac{A}{x^4} which is not true. In fact x^2\frac{A}{x^2} = A So (x^2-A/x^2)(x^2-A/x^2) = x^4 - A - A + A^2/X^4 : Missed one +-sign.
10. Find the Values of the constants in the following indentities

I assume you know that (a-b)(a-b) = (a-b)^2 = a^2 - 2ab + b^2 (*) So: (x^2 - \frac{A}{x^2}) (x^2 - \frac{A}{x^2}) = (x^2 - \frac{A}{x^2})^2 = (*) = (x^2)^2 -2x^2\frac{A}{x^2} + (\frac{A}{x^2})^2 = x^4 - 2A + \frac{A^2}{x^4} What I'm saying is that: -2x^2\frac{A}{x^2} = \frac{-2Ax^2}{x^2}...
11. Find the Values of the constants in the following indentities

(a-b)(a-b) = (a-b)^2 = a^2 - 2ab + b^2 So -2x^2\frac{A}{x^2}=-2A[/tex] not [itex]2A/X^8
12. Find the Values of the constants in the following indentities

TD: It's +2x, not -2x as in your post.
13. Find the Values of the constants in the following indentities

Just a small error. You forgot to simplify 3x-x to 2x. A(x^2-1) + B(x-1) + C = (3x-1)(x+1) <=> Ax^2-A+Bx-B+C = 3x^2+3x-x-1 = 3x^2+2x-1 <=> Ax^2+Bx-A-B+C = 3x^2+2x-1 Now try again.
14. Find the angle

If the book says sin A. Then the picture must look like this:
15. Find the angle

Shouldn't it be tan A?