Melody

Your answer for e is good 315.

My only criticism (and it may be just a person dislike) is this

If -3<x<4

then technically

3>-x>-4

this is true but I don't like the presentation.  I think the little  number should go first and that it should be rearranged and presented as  

-4<-x<3

Maybe this is just a personal bias, another mathermatician might like to comment.    

Thanks Chris,

I really like it when people ask for clarification.

It means that they are really trying to learn from our answers and that is what we want.  :)

$$\frac{(x^2+2xy+y^2)}{(x^2-y)}*\frac{(7x^2-3xy-4y^2)}{(4x^2-3xy-7y^2)}\\\\
=\frac{(x+y)(x+y)}{(x^2-y)}*\frac{(x+y)(7x-4y)}{(x+y)(4x-7y)}\\\\
=\frac{(x+y)(x+y)}{(x^2-y)}*\frac{(7x-4y)}{(4x-7y)}\\\\
=\frac{(x+y)^2(7x-4y)}{(x^2-y)(4x-7y)}\\\\$$

I don't know if it can be simplified any further.  

Thank you :)

Hi 315

c)

Consider

lim x tends to infinity of   (some little positive number divided by x)

=a little positive number divided by a huge number

the limit will be 0.

like

9/1000000000000000000000000000000000000000000000000000000000 

is a very tiny number and the more digits you add to the end of it the smaller and closer to zero it becomes.

Does that make sense?

@@ End of Day Wrap     Fri 31/10/14      Sydney, Australia       Time 4:15pm         ♬

Hi All,

There has been lots of great answers the last two days.  These were presented by Geno3141, CPhill, Alan, Will85237, Unknown, Linarose, Samanthamunguia99, reinout-g, darkangelsaura16, stormegetton, ZeroThe Protector and Kitty<3.  Thank you all.  

Now for a few interest posts:

1) This is a good question and answer  Thanks CPhill

Sat 1/11/14

1) I really liked this question.

let the number be x

double the number is 2x

subtract it from 24 and you get

24-2x

Well the quartz has displaced  186-107.5 = 78.5ml

1ml=1cm cubed

So the volume of the quartz is 78.5cm^3

5x-x^2

you cannot simplify