Math Forum / Mathematics / Undergraduate Math / August 2006

Example:  f(x){2x+1  x<0}
             {2x+2  X>(or equal to)0}
When I have to solve for f(2) I am getting two answers that work: 5 & 6, but my answer book says only 6 is right.

I am trying to solve the following systems of equations for x, y and z:
{
xyz=a
x+y+z=w

What is the generalization of the formula for the union of not-mutually
exclusive events (more than three events)?
Thanks in advance

Ok, so I know that the "formula" for the sum of complex numbers is as follows...
(a + bi) + (c + di) = (a + c) + (b + d)i
Now if I am suppose to derive the formula for the sum of two complex numbers x = (a + bi) and y = (c + di)...how can I show this?  For me, it seems that the ...

I've been running into this problem for several courses now.
The more abstract the material becomes, the more different all the different exercises become to one another -- there is less reinforcement and more creativity required.
Unfortunately, because I started out in the more ...

I took an introductory calculus course a number of years ago.  Since
that time, I have lost over 90% of what I learned in that class.
My understanding of calculus basics (derivatives, integrals, etc) is
very primitive.

I am suppose to prepare a step-by-step verification for DeMoivre's Theorem using n = 2.
Can anyone show me how to do this???

I need help with the following four evaluation questions...
1)  Evaluate [integral] (x + 1)/([sqrt](x^2 + 2x - 4)) dx
2)  Evaluate [integral] ln 3x dx
3)  Evaluate [integral] (x^2) / ((1 + x^2)^2) dx using the substitution x = tan [Theta]

how can it be proofed that the sum of each sequence 1/10^n + 1/(10^n
+1) + .....+ 1/(10^(n+1) -1) (for n = 0,1,2,3,....) is always bigger
than ln(10) ?
i.e. it will reach ln(10) when n --> infinite.

Given a differentiable convex function F ... can one prove that :
F(x) >= F(x0) + F'(x0)(x-x0)
???

can someone give me a hint about the limit of the following sequence:
lim 9^(n+2) / (10^n+9^(n+2)) for n=9 to infinite.
I strongly believe that the sequence converges but have no clue about
how to find the limit of the sequence.

Mr. Scott,
I think I understand your reasoning on the first question you helped me with
(it was a week ago - so I copied it below.  However I cannot get the correct
answer when I try to apply the same reasoning to the second problem.

plz help me
Real Analysis          
A sequence { fn } Converges to f, with respect to metric of c(X) if and only if { fn } converges to f uniformly on X.
by

Ok, so here is what I am having a hard time proving.  I honestly have a difficult time proving anything...so I would appreciate any help that you can offer.
Given:  x = r(cos u + i sin u) and y = t(cos v + i sin v)
Prove that the modulus of (xy) is the product of their moduli and ...