I don't really know how to solve this, and I have seen a duplicate of this question else where which is this:   There is only 1 answer and it doesn't really clear my doubt. Basically, what I know about squeeze theorem is this: If we have 3 functions let's say $f(x)$, $g(x)$ and $h(x)$, and the limit of each function is laid out like this:  $$\lim_{(x,y)\to(0,0)} f(x,y)\le\lim_{(x,y)\to(0,0)} g(x,y)\le\lim_{(x,y)\to(0,0)}h(x,y)$$  But in his answer, he said $$|f(x,y)|\le |x| +|y|$$ This doesn't make sense how can squeeze theorem apply here?
This is an exercise from my calculus class. The function is defined as $x\sin (1/y)+y\sin (1/x)$ if $x\neq0 $ and $y\neq0 $, and $0$ if $x=0 $ or $y=0$.  I'm pretty confident the limit exists and should be $0$, because: $$\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]=\lim_{(x,y)\to(0,0)}[x\sin (1/y)]+\lim_{(x,y)\to(0,0)}[y\sin (1/x)]$$  And: $x\leq x\sin(1/y)\leq x$, so $\lim_{(x,y)\to(0,0)}[x\sin (1/y)]=0$ right? (The same can be said for $\lim_{(x,y)\to(0,0)}[y\sin (1/x)]$)  However, I tried checking my answer, and according to Wolfram Alpha the limit doesn't exist. Is this because I'm wrong, or is it just because $x\sin (1/y)+y\sin (1/x)$ is undefined for $y\neq0 $ and $y\neq0 $
Phrase for a situation where a problem disappears when you are about to fix it, but reappears later For example, the car mechanic can't replicate the problem you are having every day, but when you drive it off the service dept, there it is again. Or, when seeing the dentist, the tooth ache goes away, and comes back when you leave. Problem on Sum of Digits of a Number I was given this problem to Prove if $Q(n)=Q(2n)$ implies $9∣n$. Where $Q(n)$ be the sum of digits of $n$. I tried to use the fact that sum of digits is congruent to the number modulo $9$ but I had no luck. Any help is appreciated. Is "Michael here" correct? Academic dishonest: Possession of unauthorized materials during an exam that you didn't even know existed So unfortunately during an exam, I had the misfortune of using an eraser (with cover) that was not mine and had a small amount of words inside it unknown to me. I did not know this was the case, as I don't have a habit of unraveling erasers or looking at them closely?  However, now I face the problem in trying to defend myself against the accusation of me cheating.  I'm specifically concerned on my university's blank statement of "possession of unauthorized materials during an exam" is considered academic dishonesty. Seems like student conduct has all the power in trying to prove academic dishonesty, despite none of my test containing any of what to me is  unreadable, small notes. In addition to whatever files I may choose to exclude, what files does the system exclude by rule or classification?    It might make sense not to backup Trash or Caches, but I'm looking for a way to tell what files are skipped "behind the scenes." Knowing if the system maintains an exclusion list or exclusion pattern would be very helpful in managing larger groups of macs. Android cancel Toast when exiting the app and when toast is being shown Can I get smaller tires without changing my rims? I currently ride a hybrid that came with 700x32c tires. Can I swap out a narrower tire without changing the rims, or do rims only fit a specific size of tire?   How small can I go before I have to buy new rims?  I hear having narrower tires makes you go quite a bit faster.  Does it really help that much? "Distribution not supported" when trying to install Intel Graphics Installer in Ubuntu Reshape three column data frame to matrix ("long" to "wide" format) Could I have a hint for testing the convergence of the following series please?  $$\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$$  I am very appreciative for your help. Bounty-like facility for rewarding excellent questions Amongst the reasons for starting a bounty, one can select:     Reward existing answer      One or more of the answers is exemplary and worthy of an additional bounty.   Why not enable one to reward excellent questions in a similar manner? "Timed Out" error when trying to join server If $g\circ f$ is injective and $f$ is surjective then $g$ is injective How to make Biber also print the debug information in the log file? I've switched from BibTeX to Biber and I was struggling with some errors.  During those problems (see  and  ) I noticed that other users seem to get a more detailed output in the log file (see e. g. ).  I also tried to run biber --tool --debug myreferences.bib, but I'm still missing those details (like the problematic source text for a FATAL error)  example of my current project  command: biber -tool --debug references.bib   INFO - This is Biber 1.9 running in TOOL mode INFO - Config file is '/Users/mbg4/.biber.conf' INFO - Logfile is 'references.bib.blg' INFO - DEBUG mode: all messages are logged to 'references.bib.blg' INFO - Looking for bibtex format file 'references.bib' INFO - Decoding LaTeX character macros into UTF-8 INFO - Found BibTeX data source 'references.bib' WARN - Datamodel: Entry '2005' (references.bib): Invalid format '2005/12//' of date field 'date' - ignoring WARN - Datamodel: Entry '2002a' (references.bib): Invalid format '2002/12//' of date field 'date' - ignoring WARN - Datamodel: Entry 'Ferri2009' (references.bib): Invalid format '2009/3/25/' of date field 'date' - ignoring WARN - Datamodel: Entry 'Klein2005' (references.bib): Invalid format '2005/9//' of date field 'date' - ignoring WARN - Range field 'pages' in entry 'Prochazaka1983' is malformed, skipping WARN - Datamodel: Entry '2006b' (references.bib): Invalid format '2006/2//' of date field 'date' - ignoring WARN - Datamodel: Entry 'Lu2001a' (references.bib): Invalid format '2001/6/15/' of date field 'date' - ignoring WARN - Datamodel: Entry 'Schubert2002' (references.bib): Invalid format '2002/9//' of date field 'date' - ignoring WARN - Datamodel: Entry 'N.N.c' (references.bib): Invalid format 'Apr\,2003' of date field 'urldate' - ignoring FATAL - Caught signal: SEGV Likely your .bib has a very bad entry which causes libbtparse to crash:    how I'd like it to look like (the FATAL - Caught signal: SEGV line):  [496] bibtex.pm:1029&gt; DEBUG - Parsing namestring 'Coyle, ,Thomas W.' [496] bibtex.pm:94&gt; FATAL - Caught signal: SEGV   Used software   TeXLive 2014 on MacOS X  biblatex v2.9a biber 1.9 $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit. Show $(z_n)_{n\in \mathbb{N}}$ converges to the same limit. $(z_n)_{n\in \mathbb{N}}$ is a complex valued sequence such that subsequences $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit.  How could I show that the sequence $(z_n)_{n\in \mathbb{N}}$ converges to the same limit using $\epsilon$, $N$ definition?    For every $\epsilon &gt;0$,  $|z_{2n}-l|&lt;\epsilon$ whenever $n&gt;N_1$, and   $|z_{2n+1}-l|&lt;\epsilon$ whenever $n&gt;N_2$.  We want to show that for every $\epsilon &gt;0$, there exists $N$ such that $|z_{n}-l|&lt;\epsilon$ whenever $n&gt;N$. I tried something like  $|z_{n}-l|\le|z_n-z_{2n}|+|z_{2n}-l|$ but wasn't sure what to do next I'm trying to make a longtable that is wider than the textwidth at a certain moment. I've tried different things always ending up with a different problem:  First possibility: If I use the adjustwidth environment the longtabu does not align correctly. The left margin stays fixed and the right margin gets out of the page. This in contrast, if I do the exact same thing to make a tabu (instead of longtabu), it works perfectly. I think using the adjustwidth is the best way to go, but I can't manage to get it working.  Second possibility: I've found a solution using the fullwidth package. That package does the trick on small longtables, but freezes when I'm trying to do it on my big longtable. The command \setlength\LTleft{-2cm} didn't work as well.  The final option I tried was to use geometry. But that changes the margin of the whole page thus making a page break which I'm not interested in. The code I used for this was  \newgeometry{left=1.2cm} \begin{longtable} long table stuff \end{longtable} \restoregeometry   Here's an example of what I want contra what I get  \documentclass[a4paper]{article} \usepackage{longtable} \usepackage{chngpage} \usepackage{lipsum} \usepackage{tabu}  \begin{document} \section{This is the original textwidth.} \lipsum[1]  \section{This is the width I need for my longtabu} \begin{adjustwidth}{-1in}{-1in} \begin{tabu} to \linewidth {*{13}{|X[l]} |} 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ \end{tabu} \end{adjustwidth}  \section{This is what happens} \begin{adjustwidth}{-1in}{-1in} \begin{longtabu} to \linewidth {*{13}{|X[l]} |} 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ 01 &amp; 02 &amp; 03 &amp; 04 &amp; 05 &amp; 06 &amp; 07 &amp; 08 &amp; 09 &amp; 10 &amp; 11 &amp; 12 &amp; 13 \\ \end{longtabu} \end{adjustwidth}  \end{document} Classifying raw LAS data as bare earth in ArcGIS for Desktop? I have a raw LAS data that has only one return (no second/ third.. return) and not classified yet. The only information I have is intensity and elevation. Is there any way that I can classify bare earth in ArcGIS? (vendor does not have more info than that). I tried classifying by selection from the profile view, but I know it is impossible to apply to all data. Generating list of manually installed packages and querying individual packages I'd like to get a list of packages installed manually by apt or aptitude and be able to find out whether a foobar package was installed manually or automatically. Is there any neat way of doing that from the command line? How can Innodb ibdata1 file grows by 5X even with innodb_file_per_table set? I have innodb_file_per_table set and just today my ibdata1 file jumped from 59M to 323M after I made several changes to an 800M table to reduce it to about 600M. That particular table's .ibd file was reduced but the server's ibdata1 file went crazy. Any ideas? Which JDK version is compatible with Netbeans on Ubuntu? I'm trying to install Netbeans on my Ubuntu. It was successfully installed but was unable to create new projects or new files. I have installed JDK 12 and then I removed it because I found here a solution that recommended removal of latest versions of JDK and set JDK 8 as default. I did what solution said but now I can't install JDK 8. It is showing me this error message:   E: Package 'oracle-java8-installer' has no installation candidate    So I started searching on the Internet about the solution and I found that "Oracle Java (JDK) 8 Installer PPA (DISCONTINUED)".   What should I do now?