How can i calculate the limit $\lim_{x \to \infty}\frac{\ln x}{x}$ without the use of delhospital rule. I have tried using the fact that $\ln x \leq x-1$ but i couldnt solve this, any help?
It seems i'm not gonna find an answer for this question which does not use LHopital's rule. How do you prove limit of (lnx)/x approaches 0 as x moves toward infinity WITHOUT using LHopital's rule?
What is the use case for a Fragment with no UI? How do you create a bootable USB stick using windows 7 I've downloaded Ubuntu desktop (the .iso file that is) on a windows 7 machine and want to create a bootable USB stick in order to install it onto a laptop which currently has no OS. Is there a way to do this? How does the garage system work in GTA V? What happens when many neurons have same weights? Does it make any sense to have two (or more) neurons in a neural network with the same weights? (intuitively it makes no sense, since all the neurons would behave the same way).   Please consider both the input and hidden layers. What if the weights are equal 0? While I basically understand what a determinant is, I wonder how this idea was developed?  What was the principal idea behind its origination?  I would like to know this so that I can have a better conceptualization of the determinant. Passing directly an array initializer to a method parameter doesn't work Javascript && operator as if statement? Why is "our today's meeting" wrong? One of the answers to  question states that &quot;We shall discuss it in our today's meeting&quot;  is grammatically correct. To me, that sentence is clearly wrong. While in today's meeting is fine and in our today meeting is OKish (though at the very least clumsy), there's something about the possessive there (our today's) that makes it wrong for me. I would read that sentence as in our today's (as opposed to your today's) meeting. Similar to in our car's trunk where the our clearly modifies car and not trunk or car trunk, the our in our today's seems to be modifying today's and not meeting. So, my questions are i) is it actually grammatically wrong to say in our today's or is it just a question of usage? and ii) if it is indeed wrong, how can we explain its wrongness? Proof a graph is bipartite if and only if it contains no odd cycles How can we prove that a graph is bipartite if and only if all of its cycles have even order? Also, does this theorem have a common name? I found it in a maths Olympiad toolbox. Why have  on every line Suppose that $f$ is differentiable on $\mathbb{R}$ and $\lim_{x\to \infty}f'(x)=M$. Show that $\lim_{x\to \infty}f(x+1)-f(x)$ exists and find it. I've been stuck on this question for a long time now and was wondering if anyone could show me how it's done. So far I have done the following: Since $\lim_{x\to \infty}f'(x)=M$ then $\forall \epsilon ,\exists A &gt;0$  s.t. if $x&gt;A$ then $|f'(x)-M|&lt;\epsilon$. So we have that $M-\epsilon&lt;f'(x)&lt;M+\epsilon$. By MVT on $[x,x+1]$ for $x&gt;A$, $\exists c\in (x,x+1)$ s.t. ${f(x+1)-f(x)\over 1}=f'(c)$. Therefore, $M-\epsilon&lt;f(x+1)-f(x)&lt;M+\epsilon$. However, I do not know what to do after this. Choosing OpenLayers or Leaflet? I was debating with one of my collegues on OpenLayers v/s Leaflet. I made a point that OpenLayers is much better API if we wish to build a project, where you need direct connectivity to the Geoserver and PostGIS.  Then I found , which looks pretty new but has the features of connectivity with the Geoserver and PostGIS.  So my project details are as follows,   Use the map interface to fetch Feature Info Create a customized tool that takes the lat/lon from user as to where he/she clicks on the map and then fetches the Climate Data from the raster (which is handled by a py script on the server) Allows user to upload excel, which is sent to the py script, which returns a GeoJSON, which creates Vector Features on the map Allow user to create vector polygons, which will fetch the Features it intersects from the WFS Layer. Fetches Layer from the PostGIS Datastore on GeoServer and displays the layers on the map.   So now I am confused on which is better and why using OpenLayers over Leaflet makes more sense or not? What wand was used by Mr Graves at the time of Fantastic Beasts? We know that the movie Fantastic Beasts is set in 1926. From the movie, we learn that at this time, Dumbledore is a teacher at Hogwarts and Grindelwald is lose after escaping a previous arrest. In the movie we learn that      Mr Graves is in fact Grindelwald in disguise. Grindelwald is shown to be at least in his forties, maybe fifties so he should already be the owner of the wand since he stole it from Gregorovitch as a teen.   We know that Dumbledore won the wand from Grindelwald after defeating him in their historic duel. That duel is always described as being “the end of the dark wizard Grindelwald” so I’m assuming that it didn’t happen prior to the movie and that he didn’t escape after that duel, please correct me if you have cannon evidence stating the contrary.      In the movie, we see Graves’ wand a few time and it isn’t the (very recognizable) one used in DH as the Elder Wand. This could of course be a prop error but since David Yates was also the director on DH and a lot of the visuals are similar I’m assuming it wasn’t. Graves could of course be using another wand in the fear that someone could recognize it but he would still be the rightful master of the Elder Wand. At the end of the movie, Newt is the one that disarms Graves/Grindelwald.   In all logic, he should have been made the new owner of the wand, whether Grindelwald was actually using it or not. That would have made it impossible for Dumbledore to win it from Grindelwald later.  So my question is: What wand is that character using at that specific time? Is he already the owner of the Elder Wand?      And if so, why wasn’t Newt made the new owner of the wand? Does Qt have a C interface? How to get Drupal 7 installed in a sub-folder / sub-directory properly? Currently i'm trying to installing a drupal 7 installation in a subfolder of another drupal public_html folder, but it doesnt seem to work. I am getting a redirect loop error in chrome. I already modified the .htaccess in the parent drupal installation to ignore the sub-folder and i also set the $base_url in the sub-directory drupal installation. How long can a temporary suspension be? I ran into a user profile that states:  This account is  to cool down. The suspension period ends on Apr 27 '24 at 7:54  At first, it seemed like a somewhat longish suspension period.  Referring to  reveals:  Depending on the severity of the problem behavior — and at the complete discretion of the moderator — your account will be placed in timed suspension for anywhere from 1 to 365 days.  This indicates that temporary suspensions can last upto a year.  Additionally, the  doesn't give any other information about the timed suspension other than the link to the wiki above. I am keen to know whether the example above (wherein the account has been suspended until 2024) is a one-off case or is it a case of documentation being obsolete? A way for "new users" to ask about their post specifically We currently require that new users have 5+ reputation to participate in meta support discussions (bugs, feedback, governance, etc). This is primarily because the use case for meta is not intrinsically obvious, so we require a modicum of "experience" with the site before jumping into it.   But that blocks new users with legitimate questions about their own posts.  Setting aside any arguments about new-users-are-evil-and-suck-the-life-out-of-our-community, I would like to propose a very specific path for new users to ask about their own question provisionally.  Instead of blocking a new user with this message:     You must have at least 5 reputation on &lt;site> to ask a question on meta.   We can change this to:     You must have at least 5 reputation on &lt;site> to post on meta, but you may ask a question about your own post specifically.      Link to your post: &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;      ask about this post   cancel    The system will check whether the linked question provided belongs to the author. . The user can then proceed with the post provided they leave the template (below) intact:     Title &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;      &nbsp;         &lt;!--Do not remove-->   &lt;!--Note: Questions not about your post will be deleted-->      I have a question about the post:       &lt;!-- Your question below: -->   &nbsp;     Not only is this a great and gentle introduction to the proper use of meta, but it stands to help new users just when they need it most (learning to use the community).   Of course this doesn't 100% guarantee that someone won't get it wrong on occasion. But this is an awful lot of in-your-face guidance without simply telling people "read our FAQ" (which they never do). And if a user manages to step over all that guidance and still manages to misuse meta, I have no compunction about summarily removing a question they should never have posted.   But this just-in-time learning is a very effective way of learning a new site in a gentle and thoughtful way. If this is abused more often than not, it is easy to disable. But it's better than assuming clueless newbie every time. What tool do you use to monitor your servers? I've got the following question:  $A = \{\sqrt{n} - \left\lfloor\sqrt{n}\right\rfloor : n \in \mathbb{N}\}$  Find inf A, sup A    inf A is no big deal, but I have a hard time proving sup A is 1  I've tried to prove that: $\sqrt{n^2 - 1} -\left\lfloor\sqrt{n^2-1}\right\rfloor &gt; \sqrt{n} -\left\lfloor\sqrt{n}\right\rfloor $  but couldn't find a way to do that I read on  that the netbook edition of Ubuntu was discontinued and that it is now integrated into the main distribution (as of 11.04).  I tried 11.04 on my new Samsung NC110-A06AU with 10.1" 1024x600 display. Most things worked out of the box, but some (like backlight power control) needed some  before they began to co-operate.  One thing that seems to be an ongoing problem is the resolution.  At 1024x600, most of the dialogue boxes run off the bottom of the screen, including the update manager. I have tried 11.10 beta 1 and it has the same problem.  Is there any way to fix this, or at least make it more usable? (I suspect not). Given the recent rise in popularity of netbooks, do you think Ubuntu will include a low-resolution-friendly version in the near future?  How well does KDE deal with these low resolutions? I noticed KDE Plasma has a netbook interface. Is it worth switching for that?