TexStudio Build & View VS Compile
What is the difference between "Build and view" and "Compile"?
If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $$\lim_{x\to\infty}f(x)=\lim_{x\to-\infty}f(x)=\infty$$  Prove that $f$ has a minimum on $\mathbb{R}$; that is, there is an $x_m\in\mathbb{R}$ such that $$f(x_m)=\inf_{x\in\mathbb{R}}f(x)&lt;\infty$$  I think the best approach would be to prove the existence of a lower bound, that is $\exists M\in\mathbb{R}:M&lt;f(x),\forall x\in\mathbb{R}$, but I don't know how to do this. I am probably supposed to use the extreme value theorem or the intermediate value theorem, but I don't know how to do that. "Die from cancer" vs. "die of cancer" Is there a difference between those expressions: "Die from cancer" or "Die of cancer"? Are they both correct? How  can I delete a node after, for example, 2 weeks it has been created? What is this operator: &= Prove that $\lim\limits_{n\to\infty}1 + \frac{1}{1!} + \frac {1}{2!} + \cdots + \frac{1}{n!}\ge\lim\limits_{n\to\infty}(1+\frac{1}{n})^n$ So My professor assigned this question and I am really stuck on part B of the question.  For $n \in \mathbb{N}$ let {$T_n$} = {$1 + \frac{1}{1!} + \frac {1}{2!} + \cdots + \frac{1}{n!}$}.  (a) Prove that {$T_n$} is non-decreasing.  (b) Use {$S_n$} = {$(1+\frac{1}{n})^n$} to prove that {$T_n$} is bounded above and prove that $lim_n(T_n)\ge lim_n (S_n)$   Like I mentioned I can prove part (a) simply by supposing that $T_{n+1} \lt T_n$ then after some algebra concluding the statement is false and than with one other example proving that its not strictly increasing either.  Now for part (b) I have not a slightest clue about how to solve, I assume I will have to use the expanded form of $S_n$ but thats the best I have. So please give me some hints or nudges in the right direction. I am an operator (OP) on my friends Realm. Today I tried to play and noticed that no commands would work for me, or anyone else granted OP. They only worked for the owner of said realm.   He has de-oped us and re-oped us with no cure to the problem. What's causing this?   Also another problem that when he tries to reload the realm it fails every single time, any options that would fix this problem? I have a HP-G62 B17S laptop, which has Windows 7 Home Edition 64-bit.  I read on a blog about a setting in msconfig.exe (Windows System Configuration utility):     Boot > Advanced options > Number of Processors   This was showing 1 for me but I have a dual core AMD Turion, so I changed the setting to 2. Next to it was a Maximum Memory setting (which was unchecked). I checked it and made sure it was max 4096; my system has 4GB RAM.  After restarting the laptop, it now gives an error:     Windows Error Recovery   Windows failed to start   I can choose from two options:   Launch Startup Repair Start Windows normally.   When I select Startup repair, it goes on to give another error:     Windows Boot Manager       Windows failed to start. A recent hardware or software change might be the cause. To fix the problem:         Insert your Windows installation disc and restart your computer.    Choose your language settings, and then click "Next."     Click "repair your computer."      I do not have the Windows installation disc for this OS version - the manufacturer did not send it to me when I purchased the laptop.  If I try to start Windows normally it takes some time and then gives the same error message.  I tried inserting another installation disc of Windows 7 Professional Edition 64-bit (available from my other laptop), and restarting, but no repair menu comes up.  I also tried restarting the laptop, pressing F8 to enter Advanced Startup Options and selecting to boot with the Last known good configuration, or starting in safe mode - neither option gives any success. This time it gives a Blue Screen of Death with the following message:     A problem has been detected, and Windows has been shut down to prevent damage to your computer - BAD_SYSTEM_CONFIG_INFO   It then does a crash dump of the memory and restarts with the same options of repairing or starting Windows normally as earlier.   What exactly seems to be the problem here and its cause? What are my options now to restore/repair my Windows 7 OS to a working condition? Would the manufacturer send a recovery/repair disk for this if I called them? The laptop should be in warranty period - it was purchased six months ago. I have a Ubuntu 10.04 bootable CD. Is there any way to boot into Ubuntu, and repair Windows from there? Are there any other way to recover the OS? (I have an access to a working Windows Vista HP Laptop, if that helps)   EDIT Ok, it was able to boot through the Win-7 professional Installation disc, but even after doing Startup repair, and System restore, It still does not boot into the original Win-7. If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$. Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$  I havent covered galois theory, this is an exercise from the chapter algebraic extensions in gallian.  I can see that $\sqrt[3]{2} + \sqrt[3]{4}$ $\in \mathbb{Q}(2^{1/3})$, after this I am clueless.  Need hints will finish the proof. In the PHP manual, to show the syntax for functions with optional parameters, they use brackets around each set of dependent optional parameter. For example, for the  function, the manual reads:  string date ( string $format [, int $timestamp = time() ] )   Where $timestamp is an optional parameter, and when left blank it defaults to the  function's return value.  How do you go about creating optional parameters like this when defining a custom function in PHP? How to copy modifiers with attribute values from active object to selected objects with python scripting? Can I start and stop a tile floor job? I am tiling my bathroom floor and don't soon have a full day to dedicate to the job. Is it ok to lay down a few tiles each day and come back to the job when I have time? I would only lay mortar for the tiles I have time to lay each day.    My concern is that the mortar wouldn't properly "join" to the previously laid sections of tile and cause an inferior result, but I'm not really basing this concern on any facts. That is what I'm hoping to learn with this question. I'm getting a NoSuchMethodError error when running my Java program.  What's wrong and how do I fix it? if $x_i$ are IID  continuous random variables, with $E[x_i]=μ$, is the following correct?   $E\left[\prod_{i=1}^n(1+⍺\space x_i)^i\right] = \prod_{i=1}^nE\left[(1+⍺\space x_i)^i\right] =  \prod_{i=1}^n(1+⍺\space E\left[x_i\right])^i = (1+⍺\space μ)^n$  thanks! Find the area of the shaded region in the figure below: Find the area of the shaded region in the figure below:    I am completely stuck on how to start off this question. Please help on some guidance on how to start it off. How to retrieve multiple rows from database in PHP Advanced search in Google Contacts Is there any way to do perform advanced searches in Google Contacts?  For example, wild card operators, AND operator, OR operator etc?  I want to search anywhere in a name, not just the beginning of a name. (i.e if I write 'ac' it should display Jack as well) We have been using this result without proof in my class, but I don't know how to prove it. Could someone point me in the right direction?  $$|1-e^{i\theta}|\le|\theta|$$  I believe this is true for all $\theta\in\mathbb{R}$. It is easy to show that the left side is bounded by 2 (triangle inequality), but I'm stuck otherwise. As shown in various episodes ("Mirror, Mirror," "Phantasms," etc.), other universes exist, oftentimes containing the same characters, albeit in different situations than in the prime universe. I'm curious, though, whether individuals that apparently exist outside of the multiverse, such as members of the Q, would not be duplicated elsewhere. It seems reasonable to me, but I'm not sure. Installing to SDCard by default I would like to know whether there is a way to tell Android to install applications on the micro SD card by default instead of having to download applications to internal memory first and then having to move them to the SD card manually.  Thanks