Math Forum / Mathematics / Undergraduate Math / February 2005

Okay, I feel like a bit of an idiot here, but I can't remember the exact
trick to integrating a piecewise function. I know it has to do with
adding the two terms together, but I'm drawing a blank *here*...
say I have f(x) = x, 0<x<20

Can you help me solve the following equation please?
(sin x)^3 + (cos x)^3 = 1
x - ?
I start with replacing 1 with (sin x)^2 + (cos x)^2, but i have no

How do you show that:
Suppose the sequence m_k is nonnegative and is decreasing
(m_k=>m_k+1) for all k in N, then show that if the sum of the series
m_k from k=1 to infinity coverges, then k times mk (km_k) coverges to

Y(x) = G(x)exp(\int_0^x Y(t) dt) + b
with b is constant. and G(x) is a known function of x.
Now, the question is how to obtain the solution of Y(x)
thanks alot

Here's the question:
The 2nd derivative test asserts that if c is a Critical Point for a
function f that is twice differentiable on neighborhood of c, then f
has a local min at c if f"(c)>0 and a local max if f"(c)<0. If

Here's a theorem:
Let R be a rectangular region in the xy-plane defined by a <= x
<= b and c <= y <= d that contains the point (x0, y0) in its
interior. If f(x,y) and pD(f)/pD(y) are continuous on R, then

Given that f_n and g_n converge uniformly to f and g respectively on
the set D subspace of Real and let c be in Real.
Prove that:
1. f_n+g_n converges uniformly to f+g on D

Given the line y = mx and a sine curve y = sin(x), I am interested in
finding a function which would provide the number of intersections
between the line and the sine curve as a function of m.  
Clearly when m = 0 there are an infinite number of intersections, but

i need help with some problems regarding rational equations please
help me

Good day, friends...
    I'm going to be starting Calculus come these next couple semesters
as an introduction to a CompSci program, but the farthest my math skills
can go is up to College Algebra (I took Trig in high school, but have

how can i find the value for x where: ln(x)=pow(e,x), that is: the
point where the graphs meet.
thx a lot in advance

can anyone help.
I'm using a text called algebra and trig by larson hostetler
i'm getting stuck in understanding the steps used to simplify the following
x-1/(x-1)-1/2

1)Calculate the limit of    f(x)={-2x  and  x<1
                                 {x^2  and  -1(<=)x(<=)2
                                 {3x-2 and  x >0           ?
2)Determine the parameters a and b that makes Lim s(x)=10,

Let ABC be any triangle , [BD] is angle bisector of <B.The length's of

I need help on my pre-Algrebra problems that i have to do tonight for
home work because i have math 2 priod tomorrow i hope some one can
help me tonight please??? I am in 8th grade so next year i am going to
be a freshman next year so please can some one help me tinight