NeonBlack

tree, it may seem stupid to you, but mathematicians can be very uptight (I don't to offend anyone ) If you are going to use l'Hopital's rule, (I don't know of any other way to do it, but their may be) you will need to take derivatives. You can't really take the derivative of [math]a_n[/math] because it is a discrete sequence, but if you have a continuous function f(x) that passes through all of the same points as [math]a_n[/math] then you can use that. Yes, I think you do need to assume that it exists, but there are a number of ways to prove whether or not it does. If a limit diverges, and you try to work with it as if it is a finite number, you may get inconsistent results.

Here is a hint to get you started: (Note: If you want to be more rigorous, define a function [math]f(x)=(1+\frac{1}{x})^x[/math] Assuming this limit exists, set it equal to say L. Take the (natural) log and then see if you can solve the limit. (You will probably also need L'hopital's rule)

[math]\frac{d}{dx} a^x=a^xln(a)[/math] or something like that.

I think I remember from my freshman biology that some antibiotics work by breaking the cell wall or by disrupting the Krebb's cycle, which is common to all organisms. I'm sure wikipedia has a lot more information on the mechanisms.

My political science professor today was saying that there are anti-despotism laws that would prevent Palin from appointing herself to the senate seat.

When discharging the maximum voltage will be 3kV (the voltage you charged it with), and the voltage will drop quickly the longer you discharge.

Right now, the unofficial tally shows Coleman up by 462 votes. There will certainly be a recount and it will probably take a long time. Both parties are assembling a team of lawyers. In other news, I heard that Ted "series of tubes" Stevens was re-elected. What happens now? Does he serve his term from prison? Does he get impeached? Do they pick someone else?

It's VERY close here in Minnesota. This is killing me. From MSN: With 40% reporting. In case you're wondering, Dean Barkley was the person appointed by Jesse V****** (We don't say his name) 6 years ago to finish Paul Wellstone's term.

Although I do support Franken, I can't exactly disagree with you for the most part. I do think your comparison of him to Rush and Moore (the 2 most disgusting figures in American politics, in my opinion) is a tad unfair though. So basically, yes, Norm Coleman is THAT BAD.

PG, Would you mind explaining what you mean by this?

There is always a small voltage drop across the diodes. Also, depending on the frequency and size of the capacitor, there will be small "bumps" in the DC output.

If you're using c++ then your #include'd headers should be <iostream> not <iostream.h> main() returns int You could easily avoid using the non-standard headers such as conio. As it is, your code will not work on most compilers. clrscr(); ^ bookworm.cpp(39) : Error: undefined identifier 'clrscr' clrscr(); ^ bookworm.cpp(505) : Error: undefined identifier 'clrscr'

Since you put this in Genetics and not math, I'll assume this is not homework. This has nothing to do with future results. Assuming the chances of having a boy or girl are equal, the odds of having a total of 3 of each is about 31%. If you want an explanation, you will have to convince me that this is not homework.

There's a difference between "we're not going to let you use our OS because you stole it" and "we're not going to let you control the way that you use our platform for trivial reasons"

Sure. Let's say we have a force [math]F=\frac{A}{x^2}-\frac{B}{x}[/math] with an equilibrium point at [math]x=\frac{A}{B}[/math] In general, the Taylor series is: [math]\sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^{n}[/math] where [math]f^{(n)}(a)[/math] means the nth derivative evaluated at a. And a is the point we want to expand around (the equilibrium point). [math]F(\frac{A}{B})=0[/math] (It's an equilibrium point). [math]F'(x)=-2\frac{A}{x^3}+\frac{B}{x^2}[/math] so [math]F'(\frac{A}{B})=-\frac{B^3}{A^2}[/math] Now we can write the force as a Taylor series up to the x term (n=1): [math]F \approx 0 -\frac{B^3}{A^2}(x-\frac{A}{B})[/math] Now use this force in Newton's 2nd law and you should get a differential equation that you recognize.

Do you know how to do a Taylor expansion? Expand the force around your equilibrium position, throwing out high-order terms. (Keeping up to the x term) Now, when you write now Newton's 2nd law, F=mx'', you should get a 2nd order differential equation with constant coefficients.

That's true.

Mass/Energy has nothing to do with it. Even without [math]E^2=p^2c^2 +m^2c^4[/math], electromagnetic waves as predicted by Maxwell 50 years before Einstein carry momentum.

For extra credit, teach your daughter this trick she can play on the teacher. Using the same cup (can't be a clear glass), while the teacher is out of the room have your daughter fill the cup with water. Then she places a stuff index card on top of it, quickly flips it over and places on the desk. With a little practice, she can do this without spilling. She carefully slides the card out from under the cup. When the teacher returns and unsuspectingly lifts the cup from the desk, water goes all over the desk. This is what I did when I was her age. Except instead of extra credit it was detention.

No, separation of variables won't work, unfortunately, because there is a term 1/2+1/4sin(t). You can do integrating factor, but (in my opinion) it's easier to do undetermined coefficients, letting Qparticular=Asint+Acost+C

I guess I'll play. Here's my laptop, WinXP SP3: Snail, that thing is called Objectdock. It's free for windows.

Look at the units it gives you for the concentration: oz(of salt)/gal(of water) Here, there is no "of what?" question, simply because it tells you. Something like 43% is dimensionless.

I was trying to be subtle so that you would see it for yourself. What you wrote as "rate in" has an additional factor of Q. This is what I am saying: (taking things directly from the problem) [math] \dfrac{1}{4} (1+\frac{1}{2} sint) oz/gal \times 2 gal/min = \dfrac{1}{2}(1+\frac{1}{2} sint) oz/min [/math] Since (you like chemistry, don't you?) amount=concentration x volume.

I'm sorry. First, you said:

i_a, you have misunderstood. Here is a better way to write that: [math]\frac{dQ_{in}}{dt}=2\frac{gal}{min}\frac{1}{4} (1+ \frac{1}{2} sint)\frac{oz}{gal}Q (oz)[/math] Do you see a problem now? This is why I prefer symbolic solutions. Well, that and I'm not very good at arithmetic.