Math Forum / Mathematics / Undergraduate Math / May 2006

I'm doing a bivariate calculus problem from a textbook. I can reach all the answers, but am unsure about something -- what does an evaluated second partial derivative mean in a marginal analysis context?
Here's the question. (I won't show all the work in reaching the answers, as ...

Let A and B be a models with alphabet {R}. Relation R^A (R^B) satisfies
i) #R^A = 3
ii) If (a,b,c) in R^A, then a,b and c all differ from each other
iii) If (a,b,c) in R^A, then (b,c,a) in R^A and (a,c,b) in R^A

I know how to convert exponentials equations into logarithmic equations and vice versa. I also know how to solve and evaluate exponential equations and logarithmic equations.
BUT I am totally stuck with the following logarithmic question. Mauybe I just don't understand what is ...

I'm not sure how to complete the following exercise.
(v)  Prove that if g1, g2, ... are integers > 1 then every
     natural number can be expressed uniquely in the form
     a0 + a1g1 + a2g1g2 + ... + akg1 ... gk

Earth revolves around the Sun in an approximately circular orbit with radius
r = a, completing a revolution in the time T = 2*(pi)sqrt(a^3/(GM) which is
one Earth year and where M = the mass of the Sun and G = the universal
gravitational constant.  The gravitational force of the ...

i have a problem doing this problem,
a right circular cylinder is inscribed in a sphere of radius r.find the
largest possible surface area of such a cylinder.
I KNOE THAT I HAVE TO MAXIMIZE THE AREA, the thing is how to find the

I am doing a chapter on bivariate calculus and so far have done about 30 problems without any mistakes. Yet I've come across one where I can't match the author's answer. Given that I've found a few typos before, I'd like to know if I'm right or wrong, and if wrong, why.
The ...

Pardon a perhaps naive question from someone who is teaching himself calculus.
I understand that the derivative of a function can be used to estimate things like marginal cost, marginal production etc.
Yet with spreadsheets, or even function-enabled calculators, available to most ...

If someone could help me out with this problem, I would be very
grateful.  My textbook gives me the following matrix:
1     3     3
-3   -5     -3

This formula only apply to value that has only the digit 9 in it(e.g 9999 or 99999999). This is the formula:
{[(q-1)9]-8-[|(y-x)|9]-[(q-1)0]-1}
Where q is the smaller no. of two.
When both no. has the same value take q as that value.

I would appreciate advice on solving the following problem.
Evaluate the definite integral:
integral (upper limit 2, lower limit 1)  [ 2x (x^2  +1 )] dx
Here is my own attempt.

Ah... the 11-sided polygon just has a prefix of Decagon.
  11-sided= undecagon
  12-sided= dodecagon...

Can the power logarithm law: log(a) m^n = nlog(a) m, be transposed to make n the subject of the equation?

Hello. I'm home-schooled and am simply curious if the books I have which I am using as my geometry course are enough to cover everything. I am quite interested in all topics in math, so I would like to make sure I'm not missing out on anything.
I have:
Geometry, Serge Lang & Gene ...

How do I calculate an improper integral? Thanks!!!!!