Integration of  $\sin^3(x)/x^3 $ from $0$ to infinity. Can it be solved using Laplace or Fourier transform ?
show that  $$\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$$  using different ways  thanks for all
Is the concept of even/odd numbers applicable to decimal numbers? For e.g. - 4.222 is a even number? I guess the proof of the identity $$ \sum_{n = 0}^{\infty} \frac{1}{n!} \equiv \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x $$ explains the connection between such different calculations. How is it done? How do I get fan control working? I know there something called fancontrol, that enables you to control the speed of your system's ventilation. I'd like to let my fans spin a bit faster as my laptop is heating up very easilly. All tutorials and stuff I've found are for old versions of Ubuntu and don't seem to be working anymore.  Can anyone explain to me or give me a good link on how I  can get it working on Ubuntu? Something different with the same effect is also fine. What if a light clock travels perpendicular to mirrors that make up the clock? "Lunch" vs. "dinner" vs. "supper" — times and meanings? I've seen cases where a noon-time meal is referred to as dinner, and the evening meal is called supper. There's also lunch around noon followed by dinner in the evening. Is there a particular difference between dinner and supper, or a circumstance where lunch becomes dinner? Custom URL Hack - anybody know how can i find the fields IDs from "User" object? I'm new in custom URL hacking.  I am trying to write a custom URL in a custom button. It is suppose to clone the User record, and while doing so, I want some user fields to be cleared. However, I need help identifying those fields IDs (e.g. Email, Name, etc).  How can i refer these fields when writing the custom URL code? Complete view of where the PATH variable is set in bash How to remove GNOME Shell from Ubuntu 20.04 LTS to install other desktop environment from scratch? I have just installed the final version of Ubuntu 20.04 LTS desktop system from ubuntu-20.04-desktop-amd64.iso. After two days of testing I completely do not like its graphical interface - the GNOME Shell. Even installation of GNOME Flashback does not help either.  So I want to completely remove the GNOME Shell with all its trails from my system without re-installation. Just want to start from scratch like it was approximately if I have installed Ubuntu from . How to reverse PCA and reconstruct original variables from several principal components? Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features from a small number of principal components?  Alternatively, how can one remove or discard several principal components from the data?  In other words, how to reverse PCA?    Given that PCA is closely related to singular value decomposition (SVD), the same question can be asked as follows: how to reverse SVD? What is the meaning of $\exp(\,\cdot\,)$? What is the meaning of the notation $\exp(\text{expression})$ ?  I think that it's something of the form $a^\text{expression}$ but does it mean that the base $a=e$ or can it be any base? Renaming files in lexicographical order with a numerical pattern that increases sequentially with fixed padding I have files such as  a bb ccc abc emrls   I would like to rename them so that, after sorting them (for example, lexicographically), each file gets the following name:  00001 00002 00003 etc   where the # of digits for the 0 padding is specified a priori, e.g. 6 in the case above (assuming that we know how many digits are needed).  Since the shell I am most comfortable with is zsh, I'm interested in solutions that benefit from features on zsh (maybe using zsh's zmv?). I would also be interested in solutions that are compatible with Bash. Let There Be Light Story Identification I am looking to identify a story that I read around 2001 (it is probably much older).  Someone showed me the story on pages printed from the internet, and it was attributed to Isaac Asimov (although I cannot state that is the true author).    The story is told in glimpses at different points of time in the future.  In each glimpse, humans are asking a more and more "intelligent" computer how to prevent the universe from collapsing into a singularity in the future, and the computer states it needs more computational power and resources to solve this problem.  At some point, man becomes one with the computer, and the computer exists in hyperspace (or subspace?).    In the final glimpse, it is the end of time and the universe is collapsing into a singularity.  At the instant the universe reaches the singularity, the computer figures out how to prevent it and says "Let there be light" and the universe begins to expand again.  Is anyone familiar with this story? Is it possible to get the sheetname? What do I need for extreme macro photography? rent a car, rent out a car, hire a car C++ iostream Corruption using stringstream What exactly is "pressure", and what's its relation to force? Where's the BIOS on an Intel Mac? I recently got a lenovo Y40 laptop and after i installed ubuntu 14.04 (also in the live usb) Wireless doesn't work. It says that it is disabled by hardware switch, however the hardware switch doesnt work (its intention is to put on airplane mode but does nothing when pressed in ubuntu) wireless works in windows and the BIOS has it enabled. I tried resetting the BIOS but it still doesn't work. Here are some command outputs  lspci:  03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 10) 04:00.0 Network controller: Intel Corporation Wireless 3160 (rev 93)   rfkill list all:   0: ideapad_wlan: Wireless LAN     Soft blocked: no     Hard blocked: yes 1: ideapad_bluetooth: Bluetooth     Soft blocked: no     Hard blocked: yes 2: hci0: Bluetooth     Soft blocked: no     Hard blocked: no 3: phy0: Wireless LAN     Soft blocked: no     Hard blocked: no   lswh:     *-network         description: Ethernet interface         product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:03:00.0         logical name: eth0         version: 10         serial: f8:a9:63:31:2e:b6         size: 1Gbit/s         capacity: 1Gbit/s         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation         configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168g-3_0.0.1 04/23/13 ip=192.168.1.4 latency=0 link=yes multicast=yes port=MII speed=1Gbit/s         resources: irq:64 ioport:4000(size=256) memory:c0604000-c0604fff memory:c0600000-c0603fff *-pci:3      description: PCI bridge      product: Lynx Point-LP PCI Express Root Port 4      vendor: Intel Corporation      physical id: 1c.3      bus info: pci@0000:00:1c.3      version: e4      width: 32 bits      clock: 33MHz      capabilities: pci normal_decode bus_master cap_list      configuration: driver=pcieport      resources: irq:59 memory:c0500000-c05fffff    *-network DISABLED         description: Wireless interface         product: Wireless 3160         vendor: Intel Corporation         physical id: 0         bus info: pci@0000:04:00.0         logical name: wlan0         version: 93         serial: a0:88:69:90:0a:38         width: 64 bits         clock: 33MHz         capabilities: bus_master cap_list ethernet physical wireless         configuration: broadcast=yes driver=iwlwifi driverversion=3.13.0-32-generic firmware=22.24.8.0 latency=0 link=no multicast=yes wireless=IEEE 802.11abgn         resources: irq:66 memory:c0500000-c0501fff Does $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent? Does the condition $\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}=1$ imply that $a_n$ convergent?  When I say convergent I mean to $L\in \mathbb{R}$ or to $\infty$ or to $-\infty$  I have a gut feeling this statement is false, just can't find a series which contradicts it.  Thanks a lot