$\lim_{x \to \infty} (x + \frac{2x^{3}}{3} - \frac{2(x^2+1)^{\frac{3}{2}}}{3})$ this limit according to wolframalpha is equal to $0$.
So this is my work thus far
$\lim_{x \to \infty} (x + \frac{2x^{3}}{3} - \frac{2(x^2+1)^{\frac{3}{2}}}{3})$ output is $\infty - \infty$ which is indeterminate for...
While reading through Analysis 1 by Vladimir A. Zorich, I encountered this proof which has this 1 step I can't understand. Here is the consequence and the proof:
For every $x\in \mathbb R$ the following is true
$$-x=(-1)\cdot x$$
Proof. $\ \ x+(-1)\cdot x=\underbrace{(1+(-1))\cdot x}_\text{Which ...
The upshot is: if analysis tag is used alongside other "analysis" tag (say real-, complex-, functional-, ....), then it gives zero extra infomation. If analysis tag is used alone, then it's not specific enough. — Arctic Char15 hours ago
@ArcticChar I understand, but nevertheless I don’t think it is deficitary in any way. Some people may explore the network using that particular tag and I put it there to reach those ones who do. Please don’t remove that tag from my posts in the future, except if I don’t put the more specific one also. Thanks for the insights on the topic — Grigori Perelman15 hours ago
I will try to do that (in general when I edit a post I do not check who's the asker - that's irrelevant). — Arctic Char15 hours ago
@ArcticChar I have copied the comment exchange into this room - so they are archived if the comments are deleted.
If you don't want to have them here, I can move them to Trash. (Alternatively, I could add you as a RO if you with to - although when I asked about that before, I did not recall some response.)
Definitely it is better to have the comment here. The comment is sort of off-topic in those posts. Yes I am happy to join as a room owner, though I have no idea what I could/should do.
@ArcticChar I think replacing instances of the analysis tag with more specific tags wherever possible is a good initiative. I was considering taking up that clean-up activity myself, but I've been a bit busy with "real" life stuff for some time now.
user185131
If some users want to keep the [analysis] tag along with other specific analysis-related tags, there is no harm in making such a compromise, provided that the tag doesn't take up a slot for a more pertinent tag.
