What can we say about $\alpha$ if $\lim_{x\to \infty}f(x)=1$ and $\lim_{x\to \infty}f'(x)=\alpha$ for a differentiable function $f$ on $\mathbb{R}$?
Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
What is the difference between the "jessie" and "jessie-updates" distributions in /etc/apt/sources.list? The  gives this example file:  deb http://httpredir.debian.org/debian jessie main deb-src http://httpredir.debian.org/debian jessie main  deb http://httpredir.debian.org/debian jessie-updates main deb-src http://httpredir.debian.org/debian jessie-updates main  deb http://security.debian.org/ jessie/updates main deb-src http://security.debian.org/ jessie/updates main   What is the difference between the jessie and jessie-updates distribution entries? I'm using a BooleanToVisibilityConverter in WPF to bind the Visibility property of a control to a Boolean. This works fine, but I'd like one of the controls to hide if the boolean is true, and show if it's false. Pretty tricky cmd The output from uname:  root@debian:~ # uname -a Linux 5asnb 2.6.32-5-amd64 #1 SMP Mon Jun 13 05:49:32 UTC 2011 x86_64 GNU/Linux   However the /sbin/init executable shows up as 32-bit:  root@debian:~ # file /sbin/init /sbin/init: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.18, stripped   Other aspects of the system seem to contradict things as well:  root@debian:~ # echo $HOSTTYPE i486  root@debian:~ # getconf LONG_BIT 32 Variation of Pythagorean triplets: $x^2+y^2 = z^3$ I need to prove that the equation $x^2 + y^2  = z^3$ has infinitely many solutions for positive $x, y$ and $z$. I got to as far as $4^3 = 8^2$ but that seems to be of no help.  Can some one help me with it? Drawing cross section in QGIS? Does anyone have a simple work-flow for drawing cross sections of earth features in QGIS?   My thing is that QGIS is being used to present the plan view, but we have a little interest in some elevations as well. All the data is one set and is simply an elevation value in the attribute table, I don't want to have to move all that to CAD.  One logical workaround is to present the z value as the y.  I am a dunce in paper space in CAD, and would be more comfortable with the QGIS Composer. Datasets constructed for a purpose similar to that of Anscombe's quartet I've just come across  (four datasets that have almost indistinguishable descriptive statistics but look very different when plotted) and I am curious if there are other more or less well-known datasets that have been created to demonstrate the importance of certain aspects of statistical analyses. How can I change directories in the terminal? How long would the conference be for? I want to know if this is grammatically correct " How long would the conference be for?". Some say that we can connect two points with a continuous curve and a small contractible neighborhood of the path together with the charts of the points can be regarded as the chart. But I don't know how to verify this statement. is piped ls the same as ls -1? ls returns output in several columns, whereas ls|cat returns byte-identical output with ls -1 for directories I've tried. Still I see ls -1 piped in answers, like ls -1|wc -l. Is there ever a reason to prefer ls -1? Why does ...|cat change the output of ls? Does opacity:0 have exactly the same effect as visibility:hidden What is the exact difference between an autoregressive (AR) and vector autoregressive model (VAR)?  I always thought that VAR would just be for more than two variables, until I learned that AR can also have more than two variables. I.e. I had a misunderstanding(?) that AR models are not always bivariate.  Before I write too much potentially false assumptions about the difference between AR and VAR, it would rather be interested to see if anyone can make provide a quick and good summary. this is my first question on PhysicsSE (I'm already an user of MathSE).   I'm a mathematics students trying to understand Faraday's law, that is   $$\varepsilon= -\frac{d \Phi_B}{dt}$$  where $\varepsilon$ means electromotive force and   $$\Phi_B=\iint \mathbf{B}\cdot d\mathbf{S}$$   means flux of magnetic field. As my textbook points out, there is an interpretation problem here: if the change in magnetic flux is due to movement of the conductor, then free charges in it are subject to Lorentz force, which then causes a current. On the contrary, if the conductor holds steady in a changing magnetic field, the induced current must be explained in terms of an electric field $\mathbf{E}$, described by the equations   $$\begin{cases} \nabla \cdot \mathbf{E}=\frac{\rho}{\varepsilon_0} \\ \nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}\end{cases}.$$  Question Do those equations hold if we have a moving conductor in a stationary magnetic field? I guess not: this would mean $\mathbf{E}=\mathbf{0}$. How to solve this? Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$ I've been given a proof that shows the following:  If $f:[a,b]\to \mathbb C$ is a continuous function and $f(t)=u(t)+iv(t)$ then $$\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$$ The proof begins by letting $\theta$ be the principle argument of the complex number $\int_a^b f(t)dt$ and there is one step in the proof I don't understand; can anyone explain to me why $$\int_a^b e^{-i\theta}f(t) dt=\Re\bigg(\int_a^be^{-i\theta}f(t)dt\bigg)$$  Would this not imply that the imaginary part of the left hand side is equal to $0$? I'm not sure why the LHS and RHS would be equal here. Imported TIF has dark gray background instead of white using QGIS 2.6  I import a TIF file, and expect the import to show an image that has black lines on a white background (with some other colors here and there), as the native windows viewer will see a white background.   The file, 49MB, imports, but   The TIF image has a dark gray background instead of a white background  I can't tell why.   Any hints?  The same thing happens if I import the TIF image into georeference, which is how I discovered this in the first place.  I created/exported the TIF image using PDFCreator (from a print of a PDF to a TIF, using that program).   Within PDFCreator, I chose a TIF export that set the color map to 4096 colors, as the default created a TIF file that was twice as large.  On testing with the default size (16 million colors or some such).... That file imported and showed the background as white.  And I can't tell why, for that, either.   Any hints?  ======== In response to the comment/question by @BradHards:  The TIFFTAG_PHOTOMETRIC is not present in either file.  The gdalinfo for the large file and small file are identical, but for the presence of two extra lines on the file where the white background turns to dark gray.  Each band sets NBITS=4 for Image Structure Metadata: eg:     Band 1 Block=5100x68 Type=Byte, ColorInterp=Red   Image Structure Metadata:     NBITS=4 Band 2 Block=5100x68 Type=Byte, ColorInterp=Green   Image Structure Metadata:     NBITS=4 Band 3 Block=5100x68 Type=Byte, ColorInterp=Blue   Image Structure Metadata:     NBITS=4   Something about the NBITS=4 state turns the background dark gray.  Alternatively, there is some other problem with the PDFCreator export.  These are the full GDALInfo:  Small with dark gray background:   Driver: GTiff/GeoTIFF Files: small file.tif Size is 5100, 6600 Coordinate System is `' Metadata:   TIFFTAG_DATETIME=2015:01:28 16:41:04   TIFFTAG_RESOLUTIONUNIT=2 (pixels/inch)   TIFFTAG_SOFTWARE=GPL Ghostscript 9.07   TIFFTAG_XRESOLUTION=600   TIFFTAG_YRESOLUTION=600 Image Structure Metadata:   INTERLEAVE=PIXEL Corner Coordinates: Upper Left  (    0.0,    0.0) Lower Left  (    0.0, 6600.0) Upper Right ( 5100.0,    0.0) Lower Right ( 5100.0, 6600.0) Center      ( 2550.0, 3300.0) Band 1 Block=5100x68 Type=Byte, ColorInterp=Red   Image Structure Metadata:     NBITS=4 Band 2 Block=5100x68 Type=Byte, ColorInterp=Green   Image Structure Metadata:     NBITS=4 Band 3 Block=5100x68 Type=Byte, ColorInterp=Blue   Image Structure Metadata:     NBITS=4   Large with white background   Driver: GTiff/GeoTIFF Files: larger file.tif Size is 5100, 6600 Coordinate System is `' Metadata:   TIFFTAG_DATETIME=2015:01:28 17:07:16   TIFFTAG_RESOLUTIONUNIT=2 (pixels/inch)   TIFFTAG_SOFTWARE=GPL Ghostscript 9.07   TIFFTAG_XRESOLUTION=600   TIFFTAG_YRESOLUTION=600 Image Structure Metadata:   INTERLEAVE=PIXEL Corner Coordinates: Upper Left  (    0.0,    0.0) Lower Left  (    0.0, 6600.0) Upper Right ( 5100.0,    0.0) Lower Right ( 5100.0, 6600.0) Center      ( 2550.0, 3300.0) Band 1 Block=5100x68 Type=Byte, ColorInterp=Red Band 2 Block=5100x68 Type=Byte, ColorInterp=Green Band 3 Block=5100x68 Type=Byte, ColorInterp=Blue Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.  Can someone help me with this? I want to install OpenOffice. What can I do to install it on my computer? Is there a word for someone that always has to be right? The person gets angry if they are not. setting upper and lower limits in rnorm