If $f(x) \geq 0$ and for every $x \in [0, \infty)$, $f(x)$ is Riemann integrable on $[0,n]$ for all n. If $\int_{0}^{\infty}f(x)dx &lt; \infty$ then is it true that $\lim_{x \rightarrow \infty}f(x) = 0$. If yes then how?
Suppose that $f:[0,\infty)\rightarrow\mathbb{R}$ is continuous. Is it true that   $$\int_{0}^\infty|f(t)|dt&lt;\infty\Rightarrow \lim_{t\rightarrow\infty}f(t)=0?$$  If so can you provide a proof, otherwise a counter example. Thank you.
Conditional conundrum A friend and I are having a debate about a most perplexing piece of English grammar. Now, I am a native English speaker, and he is Polish - this means that he is rather clued up on the grammatical side of things, whereas I know diddly squat, but know what feels right.   We were discussing Poland's next world cup match tomorrow, when Poland plays against Colombia, and I wrote to him after he me sent a heartwarming video (jokingly, of course), that 'I think threats of stoning if they don't succeed would be more effective.'  He replied that such a sentance should be in the second conditional tense, and thus go like 'I think threats of stoning if they didn't succeed would be more effective.'  So after a lively debate as to whether this is the second, first, or not even a conditional, I have no choice but to turn to the denizens of the interweb, to ask them to apply their grammatical expertise to resolve this vital question.  Thanks in advance, Conor How do I compute the principal value of a these complex numbers? I have 2 examples I'm not sure how to calculate One being $$\frac{1}{(1+i)^i}$$ the other is $$(-1+i\sqrt{3})^{1+i}$$ Can anyone help please? Anything appreciated How can I request a random row (or as close to truly random as is possible) in pure SQL? How do I create an Ubuntu live USB using a Mac? I'd like to create an Ubuntu live USB stick on a Mac to use to install Ubuntu on another machine. How do I accomplish this? My wife and I are preparing to sell our home and are discovering some weird things. Our home was built in 1958, so it is older. We found this in a corner that had some furniture in front of it.   We are wondering    What kind of wiring is this?  Is it safe to handle or remove? Correct usage of "lest" Best File Management Practices when you have thousands of Files We publish over 100+ textbooks and growing (1-color, 2-color, 4-color) maninly designed in CorelDraw &amp; Indesign with associated Image and Font Files. We also have merged multipage PDF &amp; EPS files that we send to our offset printers.Also, some Image files are exclusive to a project while some are shared across projects.   What are the best practices to follow when it comes to management of these files? We are always working on multiple versions of the same files and often with multiple DTP operators.  Right now it is all on a Shared Drive with Individual Folders but that always creates confusion in identifying the latest version of the file and some users save the file to some other folder. Security of the Data is another issue as we work with a lot of freelancers also.  How do big design studios and publishing houses handle versioning, collaboration and the associated files with a project neatly? Do they use a CMS / Document Management System? How to add "Refresh" option to right click menu in Lubuntu? I have many users at the place I work, expressing the notion of switching to Ubuntu.  Most of them, for whatever weird reason wanting to know if its possible to have refresh added when you right click on the desktop.   Is that possible? I'm very new to Ubuntu, and have come to this point that I can't boot back to my Windows Vista anymore.  I thought that I would get some kind of dual boot in the beginning when booting my computer, but this doesn't seem too happen and I don't have the slightest idea on how to fix this. I was looking for help here at askubuntu, but I couldn't seem to find anything. I'm too new with this software.  I'll need hints and tips on how to fix this  Thanks for your time folks! How do I remove all sub-directories from within a directory? This question is kind of a phase II to the first question I posted at   I have a directory that contains a bunch of sub-directories, .zip files, and other random files not contained within a sub-directory.  I'd like a command line script to remove all sub-directories from within the parent directory, but keep all zip files and loose files that don't belong to any sub-directories. All of the sub-directories have content, so I believe I'd need to force their deletion with the -f command.  So basically, a command that looks inside the parent directory (or the current directory), deletes all folders from within it, but keeps all other content and files that are not a folder or contained within a folder.  I understand that deleting items from the command line requires special care, but I have already taken all necessary precautions to back up remotely. Flawed proof that all positive integers are equal Why is there no 32 bit ISO for the new Ubuntu 18.04? How to say that you have plans to go to the movies tonight? How to say that you have plans to go to the movies tonight (but you are not sure yet, maybe you will have a pizza)? I mean there are options:     I am going to the cinema tonight.   Way too much certainty in this. For me it means that you have already bought tickets, the least.     I am going to go to the cinema tonight.   Sounds a bit awkward.     I will go to the cinema tonight.   Sounds too formal to me. "Compared with" vs "Compared to"—which is used when? Is only one of them correct? Are they used in different situations? Or are they interchangeable? When I have .txt files or .py files, I can Quick Look those files in Finder. I have .jl files that are codes written in the Julia Language. Of course they are text files. They will open in a text editor like Sublime Text. How can I Quick Look these .jl files in Finder? Including the interaction but not the main effects in a model Is it ever valid to include a two-way interaction in a model without including the main effects?  What if your hypothesis is only about the interaction, do you still need to include the main effects? Is it true that $A^A\simeq P(A)$? Let $A$ be an infinite set and $$A^A=\{f | f:A\to A\,\,\, \text{is a function}\}.$$ Is there any natural bijection between $A^A$ and $P(A)$? Your communities list is not visible in mobile web on site where you don’t have an account If you don’t have an account for some site, you can still see a list of your communities via top bar menu of this site, e.g. on 3D Printing:        But this works only for full web, in mobile web «sign up or log in» is shown:        When you have an account then the list of your communities is shown even for mobile web: Upload files upto 2GB from Apex With Ubuntu 16.04 laptop doesn't suspend when lid is closed I have a Dell 7737 laptop, and with Ubuntu 16.04 it no longer suspends when the laptop lid is closed. With 14.04 closing the lid put the laptop to suspend as expected. However, I reloaded the system with Ubuntu 16.04 and now closing the laptop does nothing. The laptop continues to run as if nothing happened.  When I manually select "Suspend" from the menu it works as expected. (Though it does prompt me to double login on resume. No, not encryption login followed by OS login. This is a double OS login.)  NOTE: Altering the System Settings|Power doesn't seem to affect anything.  Any ideas on what changed from 14.04 to 16.04 in this area?