I've tried various methods, but I couldn't get it equal to $\frac1e$. Please help!
I'm trying to find  $$\lim_{n\to\infty}\frac{n}{\sqrt[n]{n!}} .$$   I tried couple of methods: Stolz, Squeeze, D'Alambert  Thanks!  Edit: I can't use Stirling.
After the upgrade of salesforce to Spring 15, I am getting this error "Error: You have exceeded the maximum number (5) of Apex scheduled jobs." when scheduling more than 5 batches. I have this issue in several environment. I used to more than 20 batches scheduled at once.   On the link below, it says that I can schedule up to 100 batches but I am being restricted to 5 only.   I can't have more than 5 jobs here. How did Harry become a Horcrux? To make a Horcrux, certainly murder can't be the only requirement. It is obvious a proper spell is needed for completing a Horcrux. Voldemort could have made a thousand Horcruxes, as he had already murdered a thousand people. But, how on earth did Harry become a Horcrux, with Voldemort murdering his mom and not using the Horcrux-making spell? Certainly Avada Kedavra is not the spell used for making a Horcrux. How to choose trace width for very high current PCB? I am currently designing a PCB layout for my team's high current, high voltage project and am having trouble with choosing my trace width.  The circuit is composed of 12 inductors placed in series with short traces connecting them together (about 5mm max length). We are feeding 10μs pulses at ~300A/1000V at a maximum rate of 10 pulses per second by discharching capacitor banks into the coils. The capacitors are recharged by an external source.  I have looked for resources on the subject, but nothing I could find applies to the level of current and voltage we are applying.  Is there a rule for determining trace width for very high current pulses? Is the Ratio of Associative Binary Operations to All Binary Operations on a Set of $n$ Elements Generally Small? I started thinking about the number of associative (binary) operations on a set with $n$ elements today.  Looking online I found  which indicates only $113$ of the possible $19,683$ operations on a three-element set satisfy association.  So, $50\%$ of binary operations on a two-element set satisfy association, and less than $0.6\%$ of all binary operations on a three element set satisfy association.  For an $n$-element set, where $n$ denotes a natural number, is the ratio $R_{n}=A_{n}/B_{n}$, of the number of associative binary operations $A_{n}$ to the number of all binary operations $B_{n}$, in general small?  I don't mean the following questions as equivalent, but since they seem more concretely answerable in principle, does   $$ \lim_{n \to +\infty} \frac{A_{n}}{B_{n}} = 0 ? $$       Also, is $F : n \to R_{n}$ a monotonically decreasing function?  Some Background of the Question: In his Linear Algebra Problem Book 1995 on p. 6 Paul Halmos writes "The commonly accepted attitudes toward the commutative law and the associative law are different.  Many real life operations fail to commute; the mathematical community has learned to live with that fact and even to enjoy it.  Violations of the associative law, on the other hand, are usually considered by specialists only."  For all I know, Halmos might only have written that to motivate the study of Linear Algebra and doesn't quite literally mean what he appears to say.  But, if he means what he appears to say, and if $F : n \to R_{n}$ is monotonically decreasing, or $R_{n}$ is generally small, I think there's something amiss with what Halmos says, since non-associative operations seem so common that one may as well enjoy them. Additional Boxes - Criteria, Longevity, Manipulability This feature has existed for a while (I'm not sure since when exactly), but I'm mainly interested in the Gen VI implementation (hence the tag).  Usually, at the start of a game, you have some number of Boxes available. In B/W, those were 8, in X/Y I think it was 15. Under certain conditions though, you receive additional Boxes that just appear at the end of your current Boxes list. Which brings me to Part 1 of my question:     1) What are the exact conditions for additional Boxes to appear and do you always get 8 additional Boxes? (Using Pokemon Bank reveals that in X/Y, the maximum number of Boxes is 31, which I have experienced to be unlocked in 2 steps of 8 Boxes each.)   Since I'm a person who really likes to order and organize stuff, my Boxes have names and are used to categorize my Pokemon. This results in some Boxes ending up empty for a while most of the time. So here's to     2) Do additional Boxes you receive stay forever or do they disappear if the conditions for them are no longer met?      3) If they disappear, is there a way (such as renaming or putting any Pokemon in the last Box) to make them stay no matter what, even if you released all your other Pokemon? Looking for title of sci fi short story about attempts to colonise planet (Venus?). Scientist and his dog are main characters Use of Predictable Network Interface Names with alternate kernels Almost constantly, I use kernels from the , or kernels I have compiled myself, using the Ubuntu kernel configuration.  The problem is when I am using the stock kernel it seems to default to using predictable network interface names (i.e. "p4p1"), but when I use any alternate kernel it seems to default to using the old method (i.e. "eth0").  While not really relevant to this question, I had a hard disk failure on my test computer and am doing a new install of Ubuntu Server 14.04.2.  I have not been able to determine what is the difference between the kernels. I suspect a kernel configuration parameter, but have been unable to identify which one.  My question: How can I make predictable network interface names work consistently across all kernels?  Additional notes: Somewhere I saw to disable predictable network interface names to add this to grub:  GRUB_CMDLINE_LINUX_DEFAULT="net.ifnames=0 biosdevname=0"   so, I thought the opposite might help:  GRUB_CMDLINE_LINUX_DEFAULT="net.ifnames=1 biosdevname=1"   but it made no difference. Actually, I can never get the non-stock kernel to use biosdevname, no matter the setting. And I can never get the stock kernel to generate a /etc/udev/rules.d/70-persistent-net.rules file (even though, that is not what I want), no matter the setting of net.ifnames. If I have net.ifnames=1, then at least the non-stock kernel doesn't generate an incorrect /etc/udev/rules.d/70-persistent-net.rules file.  Excerpts from /var/log/udev: stock kernel:  KERNEL[9.216730] add      /devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/p4p1 (net) ACTION=add DEVPATH=/devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/p4p1 IFINDEX=2 INTERFACE=p4p1 SEQNUM=1945 SUBSYSTEM=net ... UDEV  [9.241073] add      /devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/p4p1 (net) ACTION=add DEVPATH=/devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/p4p1 ID_BUS=pci ID_MODEL_FROM_DATABASE=P8P67 and other motherboards ID_MODEL_ID=0x8168 ID_NET_NAME_MAC=enxf46d04652d8e ID_NET_NAME_PATH=enp3s0 ID_OUI_FROM_DATABASE=ASUSTek COMPUTER INC. ID_PCI_CLASS_FROM_DATABASE=Network controller ID_PCI_SUBCLASS_FROM_DATABASE=Ethernet controller ID_VENDOR_FROM_DATABASE=Realtek Semiconductor Co., Ltd. ID_VENDOR_ID=0x10ec IFINDEX=2 INTERFACE=p4p1   From Ubuntu PPA kernel 4.1RC5:  KERNEL[10.772566] add      /devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/eth0 (net) ACTION=add DEVPATH=/devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/eth0 IFINDEX=2 INTERFACE=eth0 SEQNUM=1962 SUBSYSTEM=net ... UDEV  [11.185866] add      /devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/eth0 (net) ACTION=add DEVPATH=/devices/pci0000:00/0000:00:1c.4/0000:03:00.0/net/eth0 ID_BUS=pci ID_MODEL_FROM_DATABASE=P8P67 and other motherboards ID_MODEL_ID=0x8168 ID_NET_NAME_MAC=enxf46d04652d8e ID_NET_NAME_PATH=enp3s0 ID_OUI_FROM_DATABASE=ASUSTek COMPUTER INC. ID_PCI_CLASS_FROM_DATABASE=Network controller ID_PCI_SUBCLASS_FROM_DATABASE=Ethernet controller ID_VENDOR_FROM_DATABASE=Realtek Semiconductor Co., Ltd. ID_VENDOR_ID=0x10ec IFINDEX=2 INTERFACE=eth0 SEQNUM=1962 SUBSYSTEM=net USEC_INITIALIZED=3227   Note: I have temporarily moved past this issue by allowing a /etc/udev/rules.d/70-persistent-net.rules file to be created, and then editing it for proper device names. Ultimately, I would like to get rid of the file. How to set file input value when dropping file on page? When & How often do 4e Monster powers recharge? How often should I roll power recharge rolls and at which point in the monster's turn do I re-roll them?  I'm trying to find the official definition of the recharge mechanic in the online compendium and I'm not seeing it there. E: Package 'libpng12-0' has no installation candidate [ubuntu 16.10 Gnome] I tried to install WPS Office on my laptop (ubuntu 16.10 Gnome, 64 bit) with  Gdebi installer but it said   Dependency is not satisfiable: libpng12-0   Then I tried to open this library as follows  sudo apt-get install libpng12-0   But I encountered an error:  Reading package lists... Done Building dependency tree        Reading state information... Done Package libpng12-0 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'libpng12-0' has no installation candidate   Can anyone help? Thanks a lot UK Visa in an expired Nigerian passport - what to use? I am in Nigeria, my passport will expire in 4 months and I have a document to apply for a UK visiting Visa with that passport number.  Should I use it like that or go for another passport. If I choose to get another passport, how will I use it because of the passport number on the about to expired one in the document I want to use for Visa. Could you list all possible directories where Android apps may store data, providing description what kind of data are stored in each directory? How do I stop program from skipping over getline? Bonus continent troops in Risk So I have taken over all of Australia and I get 2 extra troops.    My friend then attacks Indonesia from Southeast Asia. When it's my turn I retake control of Indonesia.  Now, do I get 2 more bonus troops since I retook control over the continent? Are there LaTeX performance profiling tools? Figure refs stop working after I added a new counter I was using the amspset document class for generating exam practice problems. I had wanted to add some referencing to the problems so I started a new counter like this (adapted from some Tex Exchange post)  \newcounter{P} \newcommand{\plb}[1]{\refstepcounter{P}\label{#1} \textbf{P-\ref{#1}.}}  \begin{problem} \plb{p1} A parallel-wire transmission line is constructed of \#6 AWG copper wire (diameter $d=0.162$ in., conductivity $\sigma_c=5.8\times 10^7$ S/m) with a 12-inch separation in air. Assuming no leakage between the two wires, find $R'$, $L'$, $G'$, and $C'$. Assume a working frequency of 1 MHz. \end{problem}  \begin{solution} Using Table.~\ref{tab:tlparam} and Fig.~\ref{fig:tlempl},  \[ Rs = \sqrt{\pi f \mu_c/\sigma_c} = 2.61\times10^{-4}~ \Omega\] \[ R' = \frac{2R_s}{\pi d} = 4.04\times10^{-2} ~\Omega\text{/m} \] \[ L' = \frac{\mu_0}{\pi} \ln{\frac{2D}{d}}=2.0~\mu \text{H/m} \] \[ C' = \frac{\pi \epsilon}{\displaystyle\ln{\frac{2D}{d}}}=5.56 ~\text{pF/m} \] $G'=0$ because the problem states that there is no leakage between the two wires. \end{solution}  \begin{figure}[ht] \begin{centering}     \includegraphics{fig24}     \caption{(Fig.2-4 from FAE) A few examples of transmission lines.} \end{centering} \label{fig:tlempl} \end{figure}  \begin{table}[ht] \caption{(Table 2-1 from FAE)Transmission-line parameters $R'$, $L'$, $G'$, and $C'$ for three types of lines.}     \begin{tabular}{c}         \hspace{3cm}\includegraphics{tb21}     \end{tabular} \label{tab:tlparam} \end{table} ... and more   Now all the figure references stop working, I get "Fig. " instead of "Fig. 1". The table references are alright though. Any idea what the problem could be? Compiling the following code and got the error of type illegal.  int main() {     // Compilation error - switch expression of type illegal     switch(std::string("raj"))     {     case"sda":     } }   You cannot use string in either switch or case. Why? Is there any solution that works nicely to support logic similar to switch on strings? Why do I get different outputs in case of sh and bash? The covid19 death data for US shows strong periodic trends. It does not make sense to me that people die periodically.   What could be the reason to having such data? I thought it might be the reporting artifacts, for example, people always update data at Monday, but the period seems to be 3-4 days. Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic. Is there a better (or other) way(s) to prove the following statement? Also, the same argument works for multiplicative groups $\mathbb{R}-\{0\}$ and $\mathbb{Q}-\{0\}$, right?       Problem Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.   Solution By cantor's diagonal argument, there is no possible bijection between $\mathbb{Q}$ and $\mathbb{R}$. Since an isomorphism needs to be a bijection, there is no possible isomorphism between the additive groups $\mathbb{R}$ and $\mathbb{Q}$.    Thanks