Math Forum / Mathematics / Undergraduate Math / December 2006

It seems to be  wellknown fact that the errors are
bounded by
m(b-a)^3 /6   and M(b-a)^5/90  (where |f''(x)|<= m  and |f''''(x)|<=M  for
all x in [a,b] ) for the trapezoid and the simpson rules but how do you

hi, can anyone think of a product that uses radicals to be made? I have to do a project on a product that uses radicals.

Theorem. Let G = (N, T, P, a) be a regular grammar, where N the set of
non-terminating symbols, T is the set of terminating symbols, P is the
set of productions and a is the starting symbol. Let
I = T

Two questions:
(1) Characterize the language generated by the following grammar:
S -> aSb
S -> Ab

[URL=http://imageshack.us][IMG]http://img451.imageshack.us/img451/385/equaxz7.gif[/IMG][/URL]

Let (A_s)_{s>0} be an open countable star-finite covering of a space X,
which admits C^infty partition of unit.
Suppose that for every s>0 there is a fixed positive real number d_s.
Can you help me in constructiong a continuous function

how do you prove that the area of the circle is pi*r^2 and that the
perimeter is 2*pi*r?
Perhaps I should have asked first how to define pi...

So the weird reality at the heart of the debates that have gone on for
years is that I say that functions like sqrt() return more than one
value while posters maintain that it has one solution--because it is
defined to have one.

[URL=http://imageshack.us][IMG]http://img167.imageshack.us/img167/7967/traperp7.jpg[/IMG][/URL]

I am stuck in figuring out the induction proof for converting binary
codes to Gray codes.
To convert binary to Gray, take the leading bit as as, and after that
xor the current and the previous binary bit tp get the Gray code bit.

 Before I'm attacked rather quickly for the ignorant question, let me
explain a bit.  I'm an undergraduate mechanical engineering student,
and I've just finished advanced math classes in multivariable calculus,
Linear Algebra, and vector calculus.  The more math I take, the more

To start with, this is my first post, I'm new here, and I have no idea if this is in the correct place. I'm 17, and a sophmore in college (community college of denver). Just a simple question that has been racking my brain because I seem to have forgotten how to do this.
You have ...

x!+y!=122 and  x-y=3  then find  (x,y)=?

I would really appreciate some help.
I haven't really done any math ( highschool math ) for almost a year but now I'm want to learn some optics and can't seem to figure out the following:
1 / a + 1 / b = 1 / f
If 'a' ( R < a <= oo ) is getting smaller then 'b' is getting bigger. I ...

To start with, this is my first post, I'm new here, and I have no idea if this is in the correct place. I'm 17, and a sophmore in college (community college of denver). Just a simple question that has been racking my brain because I seem to have forgotten how to do this.
You have ...