How to prove this? $ \lim_{x \to 0}\frac{e^x-1}{x}=1 $
How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
We can easily find out if the vectors are dependent or not by finding determinant of matrices formed from the vectors. But if the matrix is not a square matrix, we cannot find the determinant. Then how do we know if the vectors are linearly independent? Installed memory 4GB but only 1.93 GB is usable shows in system properties dialog? In my Intel Core i5 2.80 GHz CPU , DH55HC series Intel mother board machine installed with windows 7 64 bit  machine, when I right click my computer and see system properties I see that "Installed Memory(RAM): 4 GB(1.93 usable)".I have 2 x 2 GB DDR 3 RAM modules.  I have verified, * Two of RAM modules are working * Two of RAM slots in mother board are working   What are the cause(s) for this might be to look next ie: what settings in BIOS etc ? Suspended user cannot award bounty I asked a question on Stack Overflow: . I want to award my bounty to  by user  However, my Stack Overflow account is suspended recently for 7 days, and the suspension still has 5 more days to end.And I know I can't vote, ask, answer or comment as pointed on  by  with the sentence below.  You will be unable to vote, ask, answer, or comment.  I couldn't find anything about not being able to accept an answer or award bounty so I tried to accept the mentioned answer above and award my bounty to it and I got a  Suspended users cannot vote  rejection which can be seen below with a screenshot.  I know this  If you do not award your bounty within 7 days, the highest voted answer created after the bounty started with at least 2 upvotes will be awarded half the bounty amount.  from . None of the answer given to my question is upvoted and the answer I mentioned is not the oldest one after the bounty started so it won't be awarded by community. What can I do? (except being a good guy and not get suspended :)) Place each foot on a scale: can you add the two to find your weight? I frequent a blog from a British psychologist, and every Friday he likes to pose an interesting puzzle or riddle. The Monday after that he posts the answer. They're good fun, and IANAP but  made my it-might-not-be-quite-as-simple-as-that detector go off.  My question boils down to this: let's say I have two identical scales, and I stand on the scales with one foot on each scale. The scales read W1 and W2. Does my weight equal W1 + W2? If I want to display the IP address that is assigned to eth1, how can I do this in Bash? I am quite proficient with the keyboard and try to only use the mouse when necessary. Given that context I was very familiar with the shortcut keys in MS Outlook 2003 and never needed to use the mouse to use that product. Now my company has recently upgraded to MS Outlook 2010 and I am finding it impossible to operate it without having to use the mouse. In particular replying to meeting requests with the old shortcut keys no longer seems possible.   I have held down the ALT key and sometimes it shows some shortcuts on the ribbon but this seems to be limited to ALT+H which tends to alternate between designating "Accept" and "Tentative" without any keys for the other options. Also as this appears to switch between "Accept" and "Tentative" one can't even use this consistently without first having to check what it means for each particular instance.  Any help with this would be greatly appreciated! Does the canonical commutation relation fix the form of the momentum operator? For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar. $$  Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on coordinate or momentum representation, but I don't know if that statement constitutes a proof. Moreover if we choose $\hat{x}\psi=x\psi$ is the answer of the following question yes?  For the second one   $$(\hat{x}\hat{p}-\hat{p}\hat{x})\psi=x\hat{p}\psi-\hat{p}x\psi=i\hbar\psi, $$  but I don't see how can I say that $\hat{p}$ must be proportional to $\frac{\partial}{\partial x}$. I don't know if trying to see that $\hat{p}$ must satisfy the Leibniz rule and thus it should be proportional to the $x$ derivative could help. Or using the fact that $\hat{x}$ and $\hat{p}$ must be hermitian  Any hint will be appreciated. Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$ Using only rules of natural deduction, I am trying to prove that $$p \implies q \vdash \lnot p \lor q$$ but am having a lot of difficulty. I was able to prove the other direction.   Could anyone show me or point me to the right direction? Possible Duplicate:          I live in a small apartment building and we can catch each-others wifi networks. We have different service provides and were wondering if we could amalgamate our networks so that we could use each others bandwidth transparently.   I would assume this would reduce latency.  Does anybody have a tutorial on how to fuse together wifi networks for a throughput increase? The target machine is a Linux computer.   EDIT  My work makes me do lots of 1TB flat file-transfers, so I believe my motivation is sound. How do you convert a C++ string to an int? Possible Duplicate:          How do you convert a C++ string to an int?  Assume you are expecting the string to have actual numbers in it ("1", "345", "38944", for example).  Also, let's assume you don't have boost, and you really want to do it the C++ way, not the crufty old C way. Who were the hooded people in The Rise of Skywalker? Near the end of Star Wars Episode IX: The Rise of Skywalker there are several hooded figures that are shown chanting stuff (in Sith?) and just hanging out with Palpatine. Who were these people? What is the status of TTF support in Internet Explorer? Changing Screen Brightness Through Keyboard Functions on My Notebook I've installed Ubuntu 16.04 on my Asus X555LJ.  But I don't know how to install drivers or how to enable function keys to controls screen backlight brightness. How do you repair an "input/output error" in an NTFS partition? What factors determine enemy levels or: How do enemy levels scale to the player character's? When I finished Normal Mode at around Level 30 and went back to the  (still at Normal mode), I found that all enemies there are now very easy to kill, meaning they didn't level up (or hit a level cap).  When I went to  as a Level 36 character in True Vault Hunter Mode, I noticed that the enemies are the same level as me.  What factors determine enemy levels?   Specifically, I would like to know:       Are enemies affected by what level a character accepted a mission?      Or is it what level a character is when they first entered an area?      How does Normal Mode, True Vault Hunter mode, and the Ultimate True Vault Hunter Mode affect enemy levels?     Are there enemies that will scale to the player level, as the player levels up? Any enemy leveling differences specific to the DLC areas?         EDIT:   There is now  that explains how this works generally: "In playthrough 1, outside of the DLC, there's no such thing as scaling. Enemy levels are determined solely by the area they're in and your mission." Can anyone expound on that, and comment or provide an answer on what are the specific enemy levels on specific areas and/or missions?    states that "enemies do not actually "scale", or at least from what we know of..." and lists specifics for enemy levels on certain areas in the game (sans DLC areas). Can anyone expound on that and/or add specifics for enemy levels in the DLC missions or areas in TVHM (PT 2.0) and/or UTVHM? The  update has just been released, can anyone provide info about enemy levels on that mode, including the DLC areas or missions? closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$ We have previously determined that  or  can attune to magic items, but one of those is a sapient creature, and the other "always obeys your commands".  A paladin's steed (per the Find Steed spell) is also 'unusually intelligent' and falls within the score range for sapient creatures.  But what about a regular old animal? If my ranger has a wolf companion, can he make that wolf attune to, say, an Amulet of Health? According to the Beast Master archetype, a companion animal "obeys your commands as best it can".  Is spending an hour 'focused only on the item' (as required for attunement) something a beast can manage?  Or what if it's not an Animal Companion, but just a riding horse, a pet dog, a trained magpie?  I know, probably this is going to be down to the DM to determine, but is there any guidance we can use to help decide whether my cat can attune to an item, and whether rubbing it with catnip would help? Calculation of number density from material density Material density is given by $ \rho =m/V$, where $m$ is mass and $V$ is volume. Again number density given by $n=N/V$, where $N$ is the total number of particle. How can I calculate number density $n$ from material density $ \rho $. Supposing we have a table with four columns (a,b,c,d) of the same data type.  Is it possible to select all distinct values within the data in the columns and return them as a single column or do I have to create a function to achieve this? Prettify OS X console by coloring output? OS X terminal is not using colors for highlighting output from different commands, for example ls.   When compared with other systems like Ubuntu, this is a big loss of accessibility/productivity.  What solutions do I have to improve this experience? For the moment I found only this guide for  but I am looking for a more complete solution.