MaxWong

 Me too :P

Just try to be around people, they may let you join them :)

:D

My ears? They are always fine :)

Those hard integrals are what I have learnt the days I have temp. left the forum.

I knew how to do them... all of them :D

$x=1+\dfrac{1}{2+\frac{1}{1+...}}\\ 1+\dfrac{1}{x}=1+\dfrac{1}{1+\frac{1}{2+...}}\\ $

First we let x = {1;2,1,2,1,...}, then 1+1/x = {1;1,2,1,2,1,2,...}

Then we find the value of x.

$x=1+\dfrac{1}{2+\frac{1}{1+...}}\\ x=1+\dfrac{1}{2+x}\\ (x-1)(2+x)=1\\ x^2+x-3=0\\ (x+\dfrac{1}{2})^2=\dfrac{13}{4}\\ x+\dfrac{1}{2}=\pm\dfrac{\sqrt{13}}{2}\\ x=\dfrac{-1+\sqrt{13}}{2}\text{ or }x=\dfrac{-1-\sqrt{13}}{2}(rej.)\\ $

The value of the original expression is 1+1/x which is:

$1+\dfrac{2}{\sqrt{13}-1}\\ =\dfrac{\sqrt{13}+1}{\sqrt{13}-1}\\ =\dfrac{14+2\sqrt{13}}{12}\\ =\dfrac{7+\sqrt{13}}{6}$

:D

~The smartest cookie in the world.

P vs NP problem? idk

Yes :D

also, when the line is horizontal, its slope is 0,

when the line is vertical, its slope is not defined, or you can say its infinity.

When the line looks like a backslash "\", its slope is negative.

When the line looks like a slash "/". it slope is positive.

$\dfrac{d}{dx}\dfrac{3}{4(2x+7)^9}\\ =\dfrac{3}{4}\dfrac{d}{dx}\dfrac{1}{(2x+7)^9}\\ =\dfrac{3}{4}\left(\dfrac{d}{dx}(2x+7)\right)\cdot\dfrac{-9}{(2x+7)^{10}}\\ =\dfrac{3}{4}\cdot 2\cdot -9\cdot \dfrac{1}{(2x+7)^{10}}\\ =\dfrac{-27}{2(2x+7)^{10}}$

So there u go, with a denominator equals 2.

Speed = Distance/Time.

Therefore the average speed = x/p

$xy + 3x^2y+1+2xy^2+yx^2+2+yx\\ =(xy + yx)+(3x^2y+yx^2)+2xy^2+(1+2)\\ =(xy + xy)+(3x^2y+x^2y)+2xy^2+3\\ =2xy + 4x^2y+2xy^2+3$

$2x^2-(x+3)-2x(1-x)\\ =2x^2-x-3-2x+2x^2\\ =4x^2-3x-3$