Math Forum / Mathematics / Undergraduate Math / November 2005

Hi guys, what are the steps to find the following taylor series?
Find the Taylor series generated by f(x) = ln(x-2) at a=3
Step1) Find f(x), f'(x), f''(x), f'''(x)
which happens to be

Two circles intersect at points A and B. PAQ is a straight line such that points P and Q lie on the two circles. Find the locus of the midpoint of PAQ

Could anyone help to show that if n is odd then the set of all n-cycles consists of two conjugacy classes of equal size in A_n
Thx

What are the number of non-negative solutions for the equation:
a+b+c+d=12 ?
I know the combinatorics formula but how is it actually solved?

There is ABCD tetrahedron with inscribed sphere. S is a center of the
sphere, radius of the sphere equates 1 and SA>=SB>=SC. Prove that
SA>(5)^(0,5).
I can't solve it. Could you help me?

In an acuteangled triangle ABC, altitudes intersect in point H. Straight line cuts point H and interesects
AC and BC in points D and E. Perpendicular to this line intersects point H, and AB in point F. Proove that:
DH/HE=AF/FB

1.  A simple pendulum consists of a mass m swinging at the end of a
massless string of length L.  The time T for one complete swing of the
pendulum is known as the period, and if the pendulum swings through
only a small angel, the period is given by T=2(pi)sqrt(L/g) where g is

I am so strange to "Ring".
Could anyone tell me how to understand Ring?
Thanks.

I'm trying find the right equation to assess the probabilty of an event when multiple attempts are being made.
Basically, if I roll a die, i can calculate the chances of getting a 3+ followed by a 4+. But I need to calculate the chances of getting a 3+ followed by a 4+, if i roll ...

Can you please help me with these:
"The side of one equilateral triangle equals the altitude of a second triangle.. What is the ratio of their areas?"
and..
How do you prove the "Perpendicular Diagonals Theorem"?

How do you tell if a function that is approaching an asymptote goes up
or down?
f(x)=3-x/2-x
If you plug in 10 for x, it comes out to -7/-8.  Since they have the

  This was a question test on my math exam which I failed to answer
but did make lots of notes:
   Show that if n is composite, then 2^n - 1 is composite.
Now (after the test) it seems to me that this is extremely simple:

V= {(x_1, x_2, x_3, x_4, x_5) in R^5:
(x_1)-2(x_2)+3(x_3)-(x_4)+2(x_5)=0}.
How can I show that S={(0,1,1,1,0)} is a linearly
independent subset of V?

Why did you choose to major in Mathematics?

P is a point inside triangle ABC. In the triangle there is inscribed
circle which radius is greater than 1. Prove that PA>2, PB>2 or PC>2.
I don't know how to solve it. Could anybody help me?