Suppose $f:\mathbb{R} \to \mathbb{R}$ is a differentiable function such that $\lim\limits_{x\to\infty}f'(x)=1$,then is it true necessarily true that $f(x)$ unbounded?   I think that it will always intersect $y=c$ for every $c\in \mathbb{R}$ and thus cannot be bounded!
Question is :  For a differentiable function $f:\mathbb{R} \rightarrow \mathbb{R}$ what does $\lim_{x\rightarrow +\infty} f'(x)=1$ imply?  Options:    $f$ is bounded $f$ is increasing $f$ is unbounded $f'$ is bounded   I could not find counter examples but then, I strongly feel $\lim_{x\rightarrow +\infty} f'(x)=1$ would just imply that $f'(x)$ is bounded.  I do not have much idea why would other three are false.  I would be thankful if someone can suggest me some hints.  Thank You.
Include prior knowledge in regression model I've a classical dataset with real attributes and I want to perform a regression.  But, not all the entries in the training dataset are trustworthy; there is an attribute that I can turn into a confidence value (between 0 and 1) to say how much I can trust the label value. For example, if the confidence value is 0, I mustn't take the entry into consideration.  Is there a way to do this? Space before chapters and contents Is it possible to prevent an NSURLRequest from caching data or remove cached data following a request? On iPhone, I perform a HTTP request using NSURLRequest for a chunk of data. Object allocation spikes and I assign the data accordingly. When I finish with the data, I free it up accordingly - however instruments doesn't show any data to have been freed!  My theory is that by default HTTP requests are cached, however - I don't want my iPhone app to cache this data.   Is there a way to clear this cache after a request or prevent any data from being cached in the first place?  I've tried using all the cache policies documented a little like below:  NSMutableURLRequest *theRequest = [NSMutableURLRequest requestWithURL:[NSURL URLWithString:url]]; theRequest.cachePolicy = NSURLRequestReloadIgnoringLocalCacheData;   but nothing seems to free up the memory! Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$, $\forall x\in G$. Prove that $H$ is a normal subgroup of $G$.    I have tried to using the definition but failed. Can someone help me please. Is there a list of error codes for Minecraft? Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved. I'm trying to install Ubuntu 12.10 alongside Windows 7 on my ASUS laptop and I'm new to all of this.   I'm using  the Ubuntu 12.10 64-bit ISO burned onto a CD.  The first time I tried to install it, Ubuntu said it did not detect any other OS, which meant I only had 4 options:   Erase disk and install Ubuntu (I don't want to do this) Encrypt new Ubuntu. Use LVM. Something else.   If I choose the Something else option, it brings me to the partition menu and says that I have 1 disk with free space of 750516Mb (750Gb), but that's not true because I have Windows 7.  I've already read through several questions and people have mentioned that you could only have 4 primary partitions. So I got hold of partition magic and removed my D: and E:, leaving me with primary C: partition and System reserved partition and a lot of unallocated space.  I restarted the laptop several times and booted the CD again and I got exactly the same as I did previously.  How do fix this problem and install Ubuntu alongside Windows 7?  EDIT 1  Here are my results for   sudo fdisk -l; echo; sudo parted -l; echo; mount; echo; df -h   WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 750.2 GB, 750156374016 bytes 255 heads, 63 sectors/track, 91201 cylinders, total 1465149168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x90050371     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048      206847      102400    7  HPFS/NTFS/exFAT /dev/sda2          206848   146368214    73080683+   7  HPFS/NTFS/exFAT  Warning: /dev/sda contains GPT signatures, indicating that it has a GPT table. However, it does not have a valid fake msdos partition table, as it should. Perhaps it was corrupted -- possibly by a program that doesn't understand GPT partition tables.  Or perhaps you deleted the GPT table, and are now using an msdos partition table.  Is this a GPT partition table? Yes/No?     After selecting YES  Yes/No? yes                                                                Error: The backup GPT table is corrupt, but the primary appears OK, so that will be used. OK/Cancel? What's the fixed size of the suggested edit queue? We know that Stack Overflow has a suggested edit queue, visible to the users who have the  privilege. Someone said the queue has a fixed size.  What's the fixed size of the suggested edit queue?  Is it often that the queue gets filled up and users can no longer suggest edits? facl ignoring the "x" permission but only on files When I use setfacl to manage on what permissions should the children files / directories have, for some reason the files have all the permissions except the execute ("x") one.  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ getfacl . # file: . # owner: someuser # group: webs # flags: -s- user::rwx group::rwx other::rwx default:user::rwx default:group::rwx default:other::rwx  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ touch file someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ mkdir dir someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ ls -l total 4 drwxrwsrwx+ 2 someuser webs 4096 paź 31 13:35 dir -rw-rw-rw-  1 someuser webs    0 paź 31 13:35 file   I thought it has something to do with umask but changing it in various ways never gives the expected result unless I'm missing something.  How can this be fixed? Wizard sickness I remember in an interview, or during a Q&amp;A, Rowling stating that Wizards live longer than Muggles. This got me thinking about Wizard deaths in general, and then deaths being attributed to illness.  So, I ask, has there ever been a Wizard, that has died from something like cancer? Is there anything, even briefly mentioning a Wizard becoming ill?  And finally, are there any illnesses that are exclusive to Wizards? How to properly restart unity? Is it acceptable to say "fed up OF" - surely it should be "fed up WITH" or "bored WITH something" rather than "bored OF something"? AMD-V is not enabled in VirtualBox on AMD APU Develop rich API exposing Stack Overflow functionality I would love to see an actual native iPhone app for Stack Overflow, Server Fault, Super User, etc.  I've actually developed a number of iPhone apps myself, and would certainly be interested and willing in doing the bulk of the legwork, but it would be necessary for the SO team to expose a real API, instead of simply RSS feeds.  Maybe if there's enough demand behind this, we can convince the SO team to build a rich API, which could be useful for many other applications, not just an iPhone app. Diagonalizable matrix with parameters $$     \begin{bmatrix}     -2 &amp; -2 &amp; 0 &amp; 0 \\     -b &amp; -b &amp; 0 &amp; 0 \\      0 &amp; 0 &amp; -4 &amp; 4 \\      0 &amp; 0 &amp; b &amp; -b \\     \end{bmatrix} $$  I have this matrix and I need to find the values for $b$ that this matrix won't  be diagonalizable.  For what I got this matrix is diagonalizable for every $b$ value.  Please write me also the final answer, thank you very much. Is it possible to transform an armature into a curve? I have a tunnel that I want a camera to go through, and want to replace the armature with a curve so it moves exactly on that path. I'd like the camera to also rotate to follow the bends of the tunnel. Using cycles.   Appreciate it, the problem I'm having now is that the camera follows the path, but after each turn, kind of snaps back or bumps, like a recoil of sorts. I reduced the size of the turns, but it still happens. And within the graph editor I can't change the interpolation mode, it's all greyed out. The only reason it looks kind of decent is because the camera is set to 15mm. Any ideas? How do I change JPanel inside a JFrame on the fly? To put it simple, there's a simple java swing app that consists of JFrame with some components in it. One of the components is a JPanel that is meant to be replaced by another JPanel on user action.  So, what's the correct way of doing such a thing? I've tried  panel = new CustomJPanelWithComponentsOnIt(); parentFrameJPanelBelongsTo.pack();   but this won't work. What would you suggest? How can I design a tree graph with node shapes as this photo? Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$ Find the following sum : $\sum_{n=1}^{\infty} \frac{\ln n }{n(n- \ln n)}$  I couldn't find any way to solve.   I just want a hint, how to initiate? Why should I avoid multiple inheritance in C++? Is it a good concept to use multiple inheritance or can I do other things instead? Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$