I got this problem in my math.  Evaluate  $$\lim_{x\rightarrow 0} {\frac{(1+x)^{\frac{1}{x}}-e}{x}}$$  I tried applying the L'Hospital rule, to get $$\lim_{x\rightarrow 0} (1+x)^{\frac{1}{x}}\frac{1}{x^2}(\frac{x}{1+x}-ln(1+x))$$ I don't know how to proceed after this.
I tried to evaluate $$\lim_{x\to0}\frac{(1+x)^{1/x}-e}x$$but all my efforts were in vain . L'Hospital rule becomes very complicated.
rsync a file from serverC to serverA through serverB Some prestigious universities like Caltech, Stanford, MIT and Berkeley never disclose their information regarding their cut off major and cumulative GPA for M.Sc and PhD programs in engineering. I also aware of the fact that graduate schools will look at the whole package and make their decision based on sets of factors like letter of recommendation, statement of purpose as well as GPA.   However, since application fee is pretty high it is not worth it to apply to schools that you know you have a slight chance of getting into it so, I would like to know what would be the acceptable GPA (Both major and Cumulative) for applicants to be competitive for top five schools in the world? Can anyone offer any help with this..? I read it at school around 1976 but cannot remember the title nor the author. Thank you in advance!  A lone astronaut called - I think- Steve is stranded on a distant planet when his ship runs low on fuel.   His only companion is - again I think - a parrot. The fuel his ship uses is a filament or wire which is kept on a spool.   On exploring the locale he has landed in he discovers a huge building half-buried in a mountainside. He enters the building and discovers it is a museum filled with thousands of glass cases containing preserved specimens of various life forms as well as machines.   There is a robot curator that does repairs and, as the astronaut finds out, prepares cases for new exhibits.   On analysing the wire in one of the machines he discovers that is suitable as fuel for his ship so he winds a length of it onto his ships spool and leaves the planet just ahead of the robot collecting him and his parrot as museum exhibits... Proof: Every convergent sequence of real numbers is bounded Quadrilateral problem with midpoints of diagonals For an arbitrary convex quadrialteral $ABCD$:   $$AF=FC, BE=ED, GI=IH$$  Prove that points $F$, $E$ and $I$ are collinear.  I was able to solve the problem by using vectors and I think that it can be also solved analytically but I wanted some more elegant proof, more in the spirit of Euclid. How can I reliably and accurately identify the passive voice in writing or speech? Spoiler warning!  During the first escape attempt in Portal 2 (when GLaDOS is still in charge) she opens a door for you which you can choose to go through instead of following Wheatley (the blue-eyed ball). What happens if you go there? Is there a function in python to split a word into a list? Looking for Scifi Short Story in a Jerry Pournelle edited Anthology I'm looking for the title of the short story, and any of the volumes of anthology it may have appeared in. I know for SURE it's in one of Jerry Pournelle's anthologies, either Star Empires and There will be War, but as I have all the eBook version of THere will be war, I'm almost certain it wasn't there.   Anyway, the book is about a Commodore who went back to the academy to visit. I'm not sure what his name was, but I'm pretty sure he lived at "Mercer Hall". He had 2 roommates, and a butler to take care of all their needs, like putting away their stuff. (He even tried to argue with the hall monitor) The butler once took away their bottle of booze UNTIL they study for mid-term, and only gave it back AFTER they wrote to their mother AFTER the exam.   The book also goes heavily into "Bless you!" or the translated version, "May the great cosmic magnificence be benevolent toward you" or something like that. Basically, it's about as inoffensive as possible, and if you say it enough, and the aliens are reasonable, they will give up and things will resolve peacefully.   My Google-fu is weak and I can't find this particular story, or which volume of anthology was it in.   Little help? A Jamaican committed marriage fraud about 30 years ago by marrying a US citizen in a marriage where the groom was paid a certain amount of money to marry her. The groom got in legal trouble for an unrelated matter, and the marriage fraud was discovered and the family friend was deported back to Jamaica. She no longer has any paperwork involved with the deportation and she can’t remember any of the details. I do not know if she simply agreed to return to Jamica when the fraud was discovered, or if she made any attempts to mount any type of legal defense in the case. I do know that she was cooperative with the immigration authorities and that they did not have to come looking for her. She would like to come the USA for a two-week visit. The main purpose of the visit is for her to visit a friend (US citizen) who is terminally ill.  I have been looking at 8 U.S.C. 1182 and from my reading of it, it would seem that she would not be admissible to the US because of the previous immigration fraud. My understanding is based on the section that says:     In general.-Any alien who, by fraud or willfully misrepresenting a material fact, seeks to procure (or has sought to procure or has procured) a visa, other documentation, or admission into the United States or other benefit provided under this Act is inadmissible.   What’s not clear to me is if this means that she would be inadmissible permanently or if this would be subject to the 10 year limit.  Can anyone help provide some clarity on this?  If the ban is not permanent are there any tips to being able to increase her chances of being able to get a visa.  She intends to honestly answer all questions during her application process for a visa. How to partition my hard drive for Ubuntu use? Till now I was windows user. From now on I want to use only Linux.   I have 500Gb HDD. How do I partition it properly? I read that there is no right or wrong way, but still, I am confused. I did something and I have primary partition mounted on / (160Gb) which I believe is a OS and 350Gb extended partition of which I have 4Gb of swap and 346Gb mounted on /home.  I got used to C:\ and D:\ partitioning, but I don't see file system in that way. I am lost. Where is what? How can I make C:\ partition for OS and D:\ for apps, movies, music, photos. Or what I want is Windows way and I have to get used to Linux way? How to check if PHP array is associative or sequential? PHP treats all arrays as associative, so there aren't any built in functions. Can anyone recommend a fairly efficient way to check if an array contains only numeric keys? 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Today, the same thing happened again, just that nearing the capacity of the card, it failed one last time and the camera was subsequently unable to read it anymore. Despite reinsertion.  My other CF cards never once exhibited this problem, so it's pretty much isolated to this card.  The card is similarly unrecognisable on my computer CF card reader. I think the filesystem is toast, but I suspect the photo files are still intact. I would like to find ways where I can inspect the raw binary data in the card and hopefully recover the photos? How do I run 32-bit programs on a 64-bit Debian/Ubuntu? I have a 64-bit (amd64 a.k.a. x86_64) Debian or Ubuntu installation. I need to run 32-bit (i386/i686) programs occasionally, or to compile programs for a 32-bit system. How can I do this with a minimum of fuss?  Bonus: what if I want to run or test with an older or newer release of the distribution? How do I turn off equation auto numbering 'The average person' or 'an average person'? 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