Math Forum / Mathematics / Undergraduate Math / July 2005

I've seen in some computational geometry libraries equate
cramer's 3 point determinant (aka signed triangle area)
to the following:
3 point determinant = (x2-x1)*(y3-y1)-(x3-x1)*(y2-y1)

  The question is: Prove that A and A' have the same eigenvalues.
                   What, if anything, can we say about the associated
                   eigenvectors of A and A'?
  The proof is simple and what about the second question.

If f(x+y)=f(x)+f(y) for all real number x,y
and f is continuous at x=0,
Then, How to show f is uniformly continuous on reals ?
Could someone give me some hint or explanation ?

Does anyone have any info on(or experience with) using a tablet pc in
the math classroom?
Can the handwriting recognition software recognize and insert
mathematical symbols?

For rational number to be a root( potential ) of polynomial its numerator must be a factor of constant term , and its denominator must be factor of leading coefficient
Example
12*x^3-41*x^2-38*x+40 == (x-4)(3x-2)(4x+5)
where 5 is a factor of 40 and 4 factor of 12 etc...

I'm very stuck on two integrels that occur in the
section on integration by parts. They are:
Int[ln(x^2 + 4]dx and Int[x * arctan^-1 x]dx
The problem I am having is that I can expand them into

Anyone know where I can purchase a copy?  This would be for the 1991/2 edition.

Suppose f: R->R satisfies f(x+y)=f(x)+f(y)
 for all x,y in R.
We know that f(x)=kx if f is continuous at 0.
Could you show me an f which is discontinuous at 0?

I tried to solve the following two problems with little luck . I hope you can help
A)Rhombus has circle with radius r = 6   inscribed inside of it.The difference between angles alpha and beta is
" a - b = 32.5 "
Find values of diagonals e and f

One of the ways to compute the area of rhombus is with
S = ( e * f ) / 2
where e and f are diagonals of rhombus
Can someone exaplain how this formula gives you an area for rhombus ?

When E={1/n : n in Naturals},
If f:E->R definded as f(x)=x+1,
Q1>
Is there limit of f at x=0 ?

Integral Cos^5 x dx
Integral Cos^2 x Cox ^2 x Cos x dx
Substitute based on identity Cos^2 x + Sin^2 x = 1
Integral (1 - Sin^2 x) (1 - Sin^2 x) Cos x dx

Let p_n = [1-1/(2^1)][1-1/(2^2)]...[1-1/(2^n)],
and let p = lim(p_n).
Can we write p in a closed form?
Thanks.

i know its possible to re-order the rows of a matrix using permutation
matrices, but are there permutation matrices that can re-order columns too?

Find radius convergence of
Sum_(n=0 to INFINITY) a_n*x^n,
where a_n=1 ,when n=m^2, m in Naturals
     a_n=0 ,when n=/=m^2, m in Naturals