We recently discussed completion in my analysis class and I have a brief question on the subject. The completion X* of the metric space X is defined to be the set of Cauchy sequences of X with a defined equivalence relation ({xn}~{yn} if lim d(xn,yn)=0) and metric (D([xn],[yn])=lim d(xn,yn)). I...
I'm trying to understand how to interpret multidemensional limits. For example, suppose you have the following:
\lim\limits_{x \to \infty}\lim\limits_{y \to \infty} x\frac{1}{y}
Would this be infinity, 0, or 1?
This is really a more general version of the question I'm working with...
Wow, so many responses! I'll probably check out one of the books that's been mentioned; there's definitely a lot I don't know about relativity that'd be useful, I think. Thanks to everyone for all the information!
Well I think it's enough to answer my question that you can't ignore relativity. (I have seen that Simpsons episode, I love that show ^.^) But if anyone can explain the relativistic effects, I'd love to learn.
That's what I was originally thinking, since as long as you provide a force that keeps up with the gravitational force, any velocity should do.
This is the part I don't quite understand. I'm only familiar with classical mechanics, so that may be where I get lost, but since both masses are...
It seems to me that whenever I've been taught or told anything about black holes, I'm given the impression that once inside a critical radius, it would be impossible to ever escape. But I've been thinking about this, and that doesn't seem like the whole story. Granted I'm not a physicist, so...
Hmm, that seems to make sense, but it gets me to an integral I'm not having much more luck with. The only thing I can think of is some other subsitution that I can't figure out.
- 2k\int {\frac{{t^8 - 4t^6 + 2(8k - 5)t^4 - 4t^2 + 1}}{{(1 + t^2 )^3 (1 - \frac{{4kt^2 }}{{(1 + t^2 )^2...
Limits
Hmm, don't think I've learned about contour integration yet. I'll look that up. I didn't mention it before, but the integral I'm working with actually does have limits from 0 to \phi if that helps.
I'm working on a problem that I've almost completed except for a single integral that I can't seem to figure out. I can plug it into mathematica and get the answer, but I'd really like to know how to work it out. So if anyone can walk me through it, I'd appreciate it.
\int\frac...