Recent content by Cosmophile

The question is certainly (hah) flawed, in my opinion. My physics class is being done entirely online, and it is questions like this which cause me to become irritated with the course. Especially when it is my performance in this class which will go on a transcript, and not my ability to solve...

Homework Statement "A calculator displays a result as 1.3250780 x10^7 kg. The estimated uncertainty in the result is +/- 2%. How many digits should be included when the result is written?" Homework Equations I'm not sure that there are any relevant equations here, aside from (maybe) Actual...

Hey, everyone! I'm helping a friend through his calculus course and we've come across something that has stumped me (see: the title). When I learned calculus, our treatment of the epsilon-delta definition of the limit was, at best, brief. Anyway, here is the problem: Given ##\lim_{x \rightarrow...

I'm afraid I don't really understand. Could you explain more explicitly, or direct me to a good resource on this?

Hey, all! I'm learning partial fraction decomposition from Serge Lang's "A First Course in Calculus." In it, he gives the following example: \int\frac{x+1}{(x-1)^2(x-2)}dx He then decomposes this into the following sum: \frac{x+1}{(x-1)^2(x-2)} =...

Hey, all. I'm doing this problem now and have a solution, but I'm worried my solution doesn't comply with the wording of the problem. I've drawn the system I used: I marked the separation for my radii arbitrarily, but made sure to not mark it such that the two halves were equal (that is, such...

I'm not familiar with "delmitting the sum." Where can I find some information on this?

The ways listed above are the simplest, in my opinion. Though, there is also a handy theorem to know: Let ##f, g## be two continuous, differentiable functions on some interval ##[a,b].## If ##f(a) \leq g(a)## and ##f'(x) \leq g'(x)## on ##(a,b)##, then ##f \leq g## on that interval. In other...

Could you (or anyone else who sees this) elaborate on the "standard principle value?" I don't understand how we can just shift the right-hand side up. Edit: I've done a bit of research and have found that there's no real sense of consensus! This surprised me. Not even the creators of top maths...

Hmm. That's so odd; why does the graph show a disconnect at ##x = 0## then?

@LCKurtz wasn't sure if you saw my edit.

So is my answer wrong? Actually, wait. I'm aware of what you're referring to, but the answer he provided was ##(-\infty, \infty)##. Clearly, that is not correct, as he is including ##0## in the interval.

This is the graph I'm seeing.

Homework Statement Find the regions of increase and decrease for ##f(x) = -3 \cot^{-1}(x)## 2. The attempt at a solution My instructor and I disagree. The answer he gave was ##(-\infty, \infty)##, while my answer was ##(-\infty, 0) \cup (0, \infty)##. My reasoning is this: ##-3\cot...

Fixed the typo, thanks! How did you deduce the rod is vertical?