I intuitively understand that the limit goes to 1 and I can solve with L'Hôpital but I can't without it. I tried to call it equal to y and rise both sides to the base e but doesn't seems to work. $\underset{n\to \infty }{\text{lim}}\frac{\ln (n+1)}{\ln (n)}$
Find the limit of $\frac{\log(n+1)}{\log(n)}$ where $n\rightarrow\infty$. Here $n$ is a natural number so I guess we can't use L'Hopital
My question is in the title: Do black holes have a moment of inertia?  I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the literature. My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors? How can I avoid Java code in JSP files, using JSP 2? How would I use Takeown to take ownership of all folders on one drive? I have a hard drive which I need to recover specific files from but all the folders in the K:\ drive are denying me access even though I took owner ship of the full drive I.E      C:\Windows\System32>takeown /F K:\   This granted me access to the drive and see the folders but I can not access any of the folders after that.   Is there a way in which I can use Takeown to apply ownership to every directory on the drive> Rounding Percentages how to pass a value to a variable that in a other variable I am getting a "bad substitution" error while running this code. I want to print the values in h_1, h_2, h_3with a for loop.  #/!/bin/bash h_1=12 h_2=13 h_3=14 for ((i=1; i&lt;=2; i++))  do   echo "${h_$i}" done Is there any way to force SQL Server NOT to mark subscriptions as inactive, ever?  It happens sporadically when there are connection issues and I don't want to have to reinitialize the subscription every time.  Note, I'm not talking about the subscriptions being marked as expired...just as inactive.  We have retention set to 0 (infinite). I'd rather have a big distribution database than have to reinitialize a 15GB database to a subscriber over the WAN. Anyway, the real issue here is that they are getting marked as inactive within just a few hours sometimes...or sometimes a few days...it seems sporadic. Is there any way to tell WHY SQL decided in its wisdom to mark them inactive? Separate long math text under sum symbol into different lines? Particle effect showing only on one side of mirrored object I'm trying to create a fur particle effect on sonic the hedgehog, and I'm using weight paints to keep it in the areas I want.   Problem: I can only get the hair effect to show up on certain random areas on model, and only on one side.  I'm using a mirror effect to keep model symmetrical, but hair only shows on one side of the mirror.  I'm new used Blender, so I don't know what all the settings for the particle effects do.  Whats going on and how do I fix it? I am currently thinking about open-sourcing a project of mine and am in the process of preparing the source code and project structure to be released to the public. Now I got one question: how should I handle the signature key for my assemblies? Should I create a new key for the open-source version and publish it along with the other files to the SVN repository? Should I leave the key out and everyone who wants to compile the code should generate his own key?  How do you handle this? I feel a little bit uncomfortable with releasing a signature key to the public. Solving $\sqrt{x+5} = x - 1$ I'm currently learning about radicals and simplifying them, and I came across this problem on the internet and tried to solve it:  $$\sqrt{x+5} = x - 1$$  So I used this logic:  $$ \begin{align} \sqrt{x+5} &amp;= x - 1 \\ x + 5 &amp;= (x-1)^2 \\ x + 5 &amp;= (x-1)(x-1) \\ x + 5 &amp;= x^2 - 2x + 1 \\ 0 &amp;= x^2 - 3x - 4 \\ 0 &amp;= (x-4)(x+1) \\ \end{align} $$  Therefore, $x = -1$ and $x = 4$ satisfy the equation $0 = (x-4)(x+1)$.  But then I tried to plug them in the original problem $\sqrt{x+5}=x-1$:  $$ \begin{align} \sqrt{4 + 5} &amp;= 4 - 1 \\ \sqrt{9} &amp;= 3 \\ 3 &amp;= 3 \end{align} $$  So using 4 works as expected, but when using $-1$:  $$ \begin{align} \sqrt{-1 + 5} &amp;= -1 - 1 \\ \sqrt{4} &amp;= -2 \\ 2 &amp;\ne -2 \end{align} $$  At what stage am I going wrong?  And according the , the solution is $x = 4$. How can I render an edge only mesh as solid lines? I have a schematic of a raspberry pi that is completely flat, no solid faces, just connected vertices.  Is it possible to render these lines somehow, so that it looks like a 2D drawing?  Maybe with freestyle? So I paid for a minecraft account and everything but when I try to log in it says that I don't have a username. Is it an email or an email that you've made just for this account? Both are in the present perfect, but one uses the verb 'to go' and the other 'to be'. Is there a rule for this?  Is there any chance that the differences between "I have been" vs. "I have gone", are differences in English dialect (I don't know if this is the right word).  Edit Could I say that North American English speakers use "I have gone", and maybe U.K speakers say "I've been"? Or vice versa. I was playing terraria today, and my friend came and deleted the my world.  Is there a way for me to recover my world? Change the URL in the browser without loading the new page using JavaScript Complex number identity by trigonometry Show that $\lvert e^{i\theta} - 1\rvert = 2\lvert\sin(\theta/2)\rvert$ by using the geometry of the triangle with vertices 0, 1, and the midpoint of the line joining 0 and $e^{i\theta}$.  I have been able to show this identity through other means, however I am stuck on how to utilize this particular triangle. Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$} Here we use infinity norm as metrics for $C[0,1]$. The professor claims that this set is compact. I can show this set is relative compact by Arzela Ascoli, i.e., for each subsequence there is a further sub-subsequence that uniformly converges to a continuous function on $[0,1]$. But it is not intuitive to me why this set is compact, i.e. the limiting function also satisfies $|f'|_\infty \le M$. Is it true that $A$ is close and therefore compact? Using apt-get to remove packages and dependencies I can join the server and sometimes the map would load for the server but i would just fall through the map and it would dissconect me and say timed out, any solutions?