Kyle

I think Taylor's theorem and whatever theorem introduced Fourier Series (not sure what it would be called) are pretty important.

Sine and cosine are important for almost any part of mathematics and physics. They are cyclical in at least two ways: First, as you can see they repeat. Choose any position on the graph. If you add or subtract 2pi to that x-value, you will arrive at the same place. For instance at x=0 you have sine at 0 and cosine at 1. At 2pi you have the same situation. This goes on forever. Secondly, when you differentiate sine and cosine you get repetition. The derivative of sine is cosine. The derivative of cosine is -sine. The derivative of -sine is -cosine. The derivative of -cosine is sine. And so on... A similar "end is the beginning" situation occurs with e^x The derivative of e^x is e^x, and so on...

You could mention a lot of stuff with complex numbers if you wanted. Like the roots of complex numbers circle around the complex plane, arriving back where they started: And e^(i theta) equals e^(i [theta + 2 k pi]) for k being an integer. Also anything involving sin or cos. Adding 2pi just brings you right back to where you were.

Thanks a lot. It's mostly gone by now but, since we're on the same floor as the laundry room, it'll probably happen again.

Someone spilled a jug of bleach down the hall and it's making the hallway smell really bad. Is there any chemical that can be dumped on it that will safely neutralize the smell or the chemical itself without producing another gas or a worse chemical?

[math] \int_{65}^{81} [(81-x)^{3/2}-16\sqrt{81-x}] \,dx=-4096/15 [/math] [math] \int_{0}^{4} (t^3-16t)(-2t) \,dt=4096/15 [/math] I wonder if there might be a technical problem with this question. I think I have the right answer and your equation confirms it. I'll ask a few more people around the dorms and see if anyone has figured out what my teacher was trying to ask.

[math]x=81-t^2[/math] [math]y=t^3-16t[/math] After asking about tangent lines, the question asks "The curve makes a loop which lies along the x-axis. What is the total area inside the loop?" I thought I was supposed to combine these equations so that there were no t's and then integrate it. I found that [math]y=(81-x)^{3/2}-16\sqrt{81-x}[/math] And, after looking at the curve, it looks like the answer for the Area should be [math]\int_{65}^{81} [(81-x)^{3/2}-16\sqrt{81-x}] \,dx=-4096/15[/math] I've tried this answer both negative and positive and it's been wrong. Maybe I haven't found the equation of the curve correctly or integrated correctly. Does anyone see my mistake?

I'm confused about something we learned in Calc today and thought someone could explain it a little. We're doing arc lengths and now the surface area of a solid formed by revolving a curve. Given any function [math]f(x)[/math] revolved about the x axis, We treated the surface area as a lot of circumferences stacked next to each other, with the radius equal to y. My teacher showed us the formula to be [math]\int_a^b f(x)2\pi\,ds\[/math] I understand the concept of ds I think, but I don't understand is why you have to use ds and can't use [math]\int_a^b f(x)2\pi\,dx\[/math]. I pictured this problem as finding the circumference then multiplying it by thickness dx to make a hollow cylinder. Since dx is pretty much nothing, this "cylinder" would have a height of zero and would be just a 2-D circle. We could add up all the circumferences to get a surface area. Why does arc length matter at all when your slices are infinitely thin?

If there are no interfaces then where is all the antimatter? Does the matter "zone" go on forever without any sign of antimatter?

Actually as long as both explinations/mathmatical modles have equal predictive capability the simplest explination is prefered. Also let me add that I'm not kyle I'm just posting on his account and his key board is a different configuration so please excuse any and all spelling mistakes.

I think all the aliens and their planets are made of antimatter.

Of course! I'd actually tried that before, but I had made a mistake integrating at that point. Thanks for the help! This has been bugging me.

I have this problem for my Calc class and, though I've done it manually and through my calculator, WeBWorK keeps telling me I'm wrong. I hoped someone could tell me if I'm interpreting it incorrectly or maybe just doing the wrong calculation. To me, this means that I must find [math]\int t^2 e^{-2 t} \ dt[/math] According to everything I've tried, this equals [math]e^{-2t}(-t^{2}/2-t/2-1/4)[/math] What am I doing wrong here?

Kate on Linux is a great program. It colors your tags and programming and makes it very easy to find where you've made mistakes. It's not a WYSIWYG but I find it very useful for Javascript, PHP, HTML, and CSS.

Wouldn't it be extremely unlikely for two chickens (or what we today would call chickens) to be born near each other at the same time? It's not like a bunch of nearly chickens had a bunch of chickens and from then on it was all chickens. It took a long time to stabilize into what we call the species today. One egg that has something with chicken DNA in it doesn't get you anywhere close to a whole new, stable species.