NBHM QUESTION 2013 Riemann integration related question
Inequalities for combinations of $\int f $ and $\int (1/f)$ where $m\le f\le M$ on an interval
Before you disagree with me with a downvote, or just want to be funny, please hear me out. From the :  The upvote privilege comes first because that's what you should focus on: pushing great content to the top. Downvoting should be reserved for extreme cases. It's not meant as a substitute for communication and editing.  I have honestly never seen a downvote reserved for an extreme case. The process is usually 1) downvote post if it's bad and don't comment. (Not much of a process, is it?) As you stay on the site longer and longer, you develop a carelessness towards downvotes (as I have), but for new users, it's really discouraging.  question inspired me to [ask balpha to] make , which is a list of users with 1 rep who have the  badge. That's the closest I could get to new users who deleted their own posts after downvotes came in. Don't get me wrong, I know the argument about being nice to new users very well, but I still believe it to be an issue. And since , users are much more inclined to go the lazy route and downvote bad questions. No alternative measures (see below) are taken, for the most part. Personally, I leave a comment and don't downvote until the asker shows no interest in fixing their post. The only other measure taken to discourage downvotes (on answers) is the -1 rep punishment to the downvoter, which is absolutely meaningless and inconsequential anyways. How are we supposed to educate new users when we don't teach them what to do, don't direct them to the FAQ, and discourage them with downvotes right off the bat?  Instead of voting down: If the post is spammy or offensive — flag it. If the question is duplicate or off-topic — flag it for moderator attention. If something is wrong, please leave a comment or edit the post to correct it.  We claim to discourage downvoting, yet I see answers like  that encourage us to downvote first and ask questions later when a question is simply unclear or effortless. It's just an awful chain reaction. A new user comes to the site asking a question, but that doesn't work out too well, so they get downvotes, delete the question in shame, and don't get the help they deserve as a fellow writer of code and programmer. Strip away the quality of the site for a moment: the core functionality of this site, and the only reason I and a lot of other users are (still) on it, is to receive and give help to/from others. I enjoy making sure fellow programmers get the answer they need, because this site has helped me get mine when I needed them. Quality can still be maintained if content is fixed rather than downvoted more often. So can we stop discouraging new users from continuing to use this site and actually start to discourage downvoting? I think we need to encourage effort towards teaching and helping new users understand the system and why their post is bad rather than slapping them in the face with downvotes that they don't know how to interpret anyways. I'm leaving ways we can do this up to others. My first thought was to increase the punishment for downvoting answers and to no longer make question downvotes free, but those wouldn't be well-received, judging by the history of similar suggestions. . Why does the logo not show up when signing up for a site and confirming the account? I'm used to creating Java Edition Minecraft maps, where NBT can be used to set many different block, item, and entity properties, like an item's CanPlaceOn/CanDestroy list, a chest's items, and more! To open my maps up to more players, I've started creating maps on Minecraft Bedrock Edition as well. But NBT is inaccessible from commands in BE, which I knew before, but didn't know how much of a problem I would have creating these complicated command chains. One of the things that I've always been doing is giving players items with custom item names, lores, enchantments, and other properties. But there is a problem. All this would have been done in NBT in Java Edition. In Bedrock, NBT is inaccessible from commands, meaning the commands I used in JE don't work. Are my dreams crushed? How do I install libtiff.so.3? When I try to run Maya from the terminal, I get:  error while loading shared libraries: libtiff.so.3: cannot open shared object file: No such file or directory.   How do I solve this?  Note: Maya is a third-party software. So I have a generic list, and an oldIndex and a newIndex value.  I want to move the item at oldIndex, to newIndex...as simply as possible.  Any suggestions?  Note  The item should be end up between the items at (newIndex - 1) and newIndex before it was removed. I wonder a generalization of Jensen's inequality: let $\mathbf{X,Y}$ be two positive definite matrices, can we obtain the following Jensen like inequality $$(1-\lambda)\mathbf{X}^{-1}+\lambda\mathbf{Y}^{-1} \succeq((1-\lambda)\mathbf{X}+\lambda\mathbf{Y})^{-1}$$ for any $\lambda \in (0,1)$, where the notation $\mathbf{A}\succeq \mathbf{B}$ represents matrix $(\mathbf{A-B})$ positive semi-definite. Return a blank when cell reference is blank I am using the following formula in a Google Sheets to calculate the number of days between two dates (dates are in columns G and AL):  =ARRAYFORMULA(if(row(A:A)=1, "Readmission Days", (G:G)-(AL:AL)))   It has to be an array because I am working with a Google Forms and entries are automatically populated into new rows.  The problem is that some of the cells in col AL are blank, so the formula is reading those dates as something else and returning a very large number. Also, when both cells are blank, the formula returns a 0, messing up my data.  How can I include something to ignore blank cells or just return a blank when one or both cell references is blank? How to have separated but vinculated multiple Ubuntu One accounts? Why are properties lost in the Cayley–Dickson construction? Is there a word for describing people who know many things but superficially? Is there an appropriate word for the antonym of "full-stack", as in programming? Someone who knows a lot of things just as a full-stack programmer, but without mastering them. I have built a peak detector circuit using op-amps/comparators to amplify the signal from an electret microphone, hold the peak signal and create a sharp logic edge when a peak is detected to be sent to a microcontroller.  I have built the circuit as follows setting up OA1 as a non inverting amplifier with a gain of 1000, but the voltage out from the OA1 remains fixed at about 4.5V no matter how much noise I make into the microphone. The comparator part of the circuit is outputting approximately 2V low and 5V high depending on how I set the potentiometer. All the components appear to be working.         &ndash; Schematic created using What potions actually grant fame or glory, or put a stopper in death? Are there any? ‘You are here to learn the subtle science and exact art of potionmaking,’ [Snape] began. He spoke in barely more than a whisper, but they caught every word – like Professor McGonagall, Snape had the gift of keeping a class silent without effort. ‘As there is little foolish wand-waving here, many of you will hardly believe this is magic. I don’t expect you will really understand the beauty of the softly simmering cauldron with its shimmering fumes, the delicate power of liquids that creep through human veins, bewitching the mind, ensnaring the senses ... I can teach you how to bottle fame, brew glory, even stopper death – if you aren’t as big a bunch of dunderheads as I usually have to teach.’&#185;   Philosopher's Stone - page 102 - Bloomsbury - chapter 8, The Potions Master   Are there any canon potions that actually grant fame or glory, or stopper death? I'm looking for specific canon-based answers from sources such as the Harry Potter books, interviews with J.K. Rowling, or information from Pottermore. Maybe because it's early I'm overlooking the obvious, but offhand I can't think of any canon potions that fit this criteria exactly.   &#185;I edited in the entire paragraph that I can teach you how to bottle fame, brew glory, even stopper death comes from for clarity. Hopefully this will be helpful and provide a better context for the comment in question. Does the series $\sum\limits_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$ converge? Does the following series converge? $$\sum_{n=1}^\infty \frac{1}{n\sqrt[n]{n}}$$   As $$\frac{1}{n\sqrt[n]{n}}=\frac{1}{n^{1+\frac{1}{n}}},$$ I was thinking that you may consider this as a p-series with $p&gt;1$. But I'm not sure if this is correct, as with p-series, p is a fixed number, right ? On the other hand, $1+\frac{1}{n}&gt;1$ for all $n$. Any hints ? Is there a way to export my artwork as PDF so that it has a transparent background? Something like exporting objects only... whenever I try to save my .ai as pdf, it always comes with a full white background. If I try to save as eps, I get a chunky white background (where it has white rectangles behind the artwork only where the artwork exists, so there are transparent chunks).  If I export as png, I get an image like what I'm looking for. Is there any way to do that in a vector format? Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$ I am wondering whether there is any difference between a gerund acting as subject and an infinitive acting as a subject. Question about Conditional Expectation Execute bash script from URL On average, how many times must I roll a dice until I get a $6$?  I got this question from a book called Fifty Challenging Problems in Probability.   The answer is $6$, and I understand the solution the book has given me. However, I want to know why the following logic does not work: The chance that we do not get a $6$ is $5/6$. In order to find the number of dice rolls needed, I want the probability of there being a $6$ in $n$ rolls being $1/2$ in order to find the average. So I solve the equation $(5/6)^n=1/2$, which gives me $n=3.8$-ish. That number makes sense to me intuitively, where the number $6$ does not make sense intuitively. I feel like on average, I would need to roll about $3$-$4$ times to get a $6$. Sometimes, I will have to roll less than $3$-$4$ times, and sometimes I will have to roll more than $3$-$4$ times.  Please note that I am not asking how to solve this question, but what is wrong with my logic above.  Thank you! I’m a big fan of ampersands (possibly too much …) and I’d like to replace all mentions of “et al.” (included in citations) by \&amp; al. – both in the main text (I use natbib citations of the form [Author1 et al., 1999]), and in the actual bibliography?  How can I do that, considering that BibTeX is inserting the words for me, and I have no control over the text? Preferably, I’d like to do this without creating my own bibliography style sheet (since I want to make this work regardless of the actual BibTeX style that is used), but if anyone can tell me how I need to edit the style sheet file, that would be fine as well (makebst doesn’t seem to offer an option for this …).