I just been victimized by a user for hate downvote. The story is like this: I reply to one question, and realise that someone suggested an off-topic answer, I downvote him and comment about the downvote.   After 10 minutes, I check back on Stack Overflow, and I realise that all my past comments and questions start getting downvoted. I lose about 20 points due to those downvotes. I accept that someone can downvote me, if they don't like my answer, but in 5-10 minutes 20-30 comments of mine from 6 month old question/comments get downvotes which means someone is doing it on purpose.
I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back?
I am stuck on how to calculate the following limit: $$\lim_{x\to\infty}x\left(\left(1 + \frac{1}{x}\right)^x - e\right).$$  Definitely, it has to be through l'Hôpital's rule. We know that $\lim_{x\to\infty} (1+(1/x))^x = e$. So, I wrote the above expression as $$\lim_{x\to\infty}\frac{\left(1 + \frac{1}{x}\right)^x - e}{1/x}.$$Both numerator and denominator tend to zero as x tends to infinity. I applied l'Hôpital's rule twice, but I got the limit equal to infinity which is clearly wrong. In the book, it says that the limit should be $-e/2$.  Any help please? Also, in case someone managed to solve it, please tell me which numerator and denominator did you apply your l'Hôpital's rule to in both cases? Thanks a lot  Also, guys can you tell me how to write equations in this forum? Thanks. Let $x \in \mathbb R$  Find a closed form of $\int_0^\infty\dfrac{\cos(xt)}{1+t^2}dt$ .   Let me give some context: this is an exercise from an improper integrals course for undergraduates. My teacher was not able to give a valid solution without  resorting to Fourier series.   He actually wanted to prove first that the function is a solution of the ODE $$ y-y'' =0$$ without succeeding in proving it.   Anyway the result sould be $\dfrac{\pi}{2}e^{-x}$  Thanks for any help on this subject. I need to delete some rows from one large table. The rows to delete shouldn't be in another table, example:  DELETE FROM LargeTable WHERE id IS NOT IN (SELECT DISTINCT foreign_id from EvenLargerTable)  but my server can't handle such blunt query, because there are almost a million records in the LargeTable and few million records in the EvenLargerTable  How can I solve it? Covariance of a variable and a linear combination of other variables Let $X,A,B,C,D$ be time-series variables and the covariance between any two pairs of these are known.  Suppose we want to find $\textrm{cov}(X,aA + bB + cC + dD)$, where $a,b,c,d$ are constants.  Is there any way of doing this without expanding out $E[(X-E[X])(aA+......)]$? prove inequality through mean value theorem (Revised) Prove that $\phi$ is a group homomorphism and find the kernel. Quoting " Let $\phi : \Bbb Z \rightarrow \Bbb Z$ be given by $\phi(n) = 7n$. Prove that $\phi$ is a group homomorphism. Find the kernel, and the image of $\phi$."   My understanding:  Part 1:   Given $n,m \in \Bbb Z$, let's check that $\phi(n+m) =\phi(n)+\phi(m)$  $$\phi(n+m) = 7(n+m) = 7n + 7m = \phi(n)+\phi(m)$$  Therefore as the group operation in $\phi$ is preserved, $\phi$ is a group homomorphism.  Part 2 (revised):   $\phi$ is one-to-one as:  $\space \space \phi (n) = \phi(m) \Rightarrow 7n =7m \Rightarrow n=m  $. We also know that $\phi(e)=e$ by the property of homomorphism. Therefore, no other object than $0$ in the domain can map to $0$ in the codomain. It follows that: $$\ker(\phi)=\{ x \in \Bbb Z : \phi(x)=e\}=\{e\}$$   Part 3 (revised):  I claim that the only possible image-elements of $\phi$ are the multiples of $7$ in $\mathbb Z$ denoted $7\mathbb Z$.   To prove this I have to show that Im$(\phi) \subset 7 \Bbb Z$ and that $ 7 \Bbb Z \subset $ Im$(\phi)$.  Proving Im$(\phi) \subset 7 \Bbb Z$ :      $\forall y \in $ Im$(\phi)$ such that $  y =\phi(x)$ where $x \in 7 \Bbb Z$. It follows that $y \in 7 \Bbb Z$, therefore Im$(\phi) \subset 7 \Bbb Z$   Proving $ 7 \Bbb Z \subset $ Im$(\phi)$:   $\forall y \in  7\Bbb Z$ such that $  y =7x$ where $x \in \phi(x)$. It follows that $y \in \phi(x)$, therefore $ 7 \Bbb Z \subset $ Im$(\phi)$.   Any input to my understanding is much appreciated. How long should I keep my tax documents, and why? Why images are blury when extracting image sequence from video clip? I have an issue when generating an image sequence from a video clip. Pictures 1,2,and 3 are three consecutive images from a video clip. Picture 4 is a close-up of the heel of one of them. The camera is on a tripod. As you can see there is no issue with the brick wall, but with any moving part there is. The camera is a Panasonic HDC-SD100. The clip is AVCHD 1920/1080. If I use VLC to extract the image sequence there is no issue. I use all the default settings except for the rendering resolution which I set to 100% and image compression to 0%. I have the issue with Blender 2.79b and 2.80. With this image issue it is impossible to do camera tracking. Any ideas what I need to do in order to solve this. Best regards. Is using Gravatar a security risk? This has been . It is unfortunate the accepted answer is so far from reality.   There are some facts:    's MD5 hash is an unsalted MD5 hash of an email address. A 3rd party could harvest every MD5 hash for every user's email on Stack Overflow.  The 3rd party could store all the hashes in a lookup table Email addresses are usually of a very particular format The attacker could start with a brute force of @gmail.com followed by @yahoo.com, etc. The attacker has the advantage that he/she could attack a huge set of emails in one go. So instead of needing to brute force every email individually the attacker can brute force in bulk.   The algorithm is quite simple, calculate a "random" MD5, look it up in the lookup table.       Is Gravatar a big enough security risk to warrant caching images locally?     Examples:    Someone could harvest about 50k email addresses quite easily and shoot off a bogus promotion from Stack Overflow to all the users. A spammer/stalker/generic evil guy can tie you identity to all the rest of the sites that use Gravatar. "(" or "\left(" parentheses? What is the difference between ( and \left( in LaTeX? Sometimes, when the content is small, it does not seem to matter which pair I use.  What is the best practice when it comes to which parentheses use? Swing's KeyListener and multiple keys pressed at the same time Is there a way to output for Print. I want to save in a higher DPI than the default 72dpi say 300dpi that's a good quality for printed pieces. I tried downloading an add-on but don't know if I am installing it correctly it isn't showing up but the bar in python is green. I'm using the 2.69 version of Blender. If no such feature exists what size have any of you found best for print quality. Thank you Product Snippets with JSON-LD + Schema.org - Are there any live examples in Google index? ** EDIT Feb 2016 - Finally JSON-LD seems to be working now in SERPS, with extremely fast changes-to-index time, assuming you have everything with Google merchant center feeds syncd and linked. Make sure the price, stock, and identifier are the same on your JSON-LD as it is on the Google shopping feed. New organization-&gt;localbusiness types are live, organization reviews are live... however JSON-LD feed alt= endpoints still do not exist, the homepage schema defining custom site name is not active, and G support for schema itemList/dateModified is still questionable. You can still get pagination results and date modified snippets by using literal text strings in your view/template Showing 1-28 of 8977 Results (321 Pages)and Last updated on February 3rd 2016. To proceed to a deeper exploration of JSON-LD support, see these:       Original Post Below: Google seems to be flip flopping JSON-LD -&gt; Schema.org product [or other types of] snippets. The snippets verify without error in both the testing tool and long term (10+ months) across 5 properties in GWT search console. The snippets have been applied to index, removed, applied, and removed again, seemingly not being applied again in regards to various facets. Since they worked in the past via microdata, and were applied long term, I assume it's due to the switch to JSON-LD. I have not found any official docs nor examples that say &quot;Google will support and render products snippets that use JSON-LD&quot;. Same thing with breadcrumb snippets and review looping. All I see is a handful of Google examples for events, movies, recipes, very basic [incomplete] organization etc. This seems strange to me considering the sheer amount of ecom pages using product snippets trumps the amount of movies, recipes, and events combined. So the question is, does Google officially support, index, and render product markup using JSON-LD? If so, can anyone point me to a live example to verify this? ** This question is not intended to be &quot;opinion/recommendation based&quot;....im looking for a specific link and subsequent SERP result [evidence] showing that JSON-LD products/etc are indeed rendered within Google.com realm as of late August 2015. ** EDIT Nov 16 2015 - Another annoying caveat has been found. Google merchant center validates certain shopping feed fields such as condition, stock, and price against live microdata. However, it seems to not recognize JSON-LD.... although, as stated above, it's recommended to use in all the G examples, and it validates the snippet test. So due to this, your merchant center account could be suspended because of &quot;differences in presentation data&quot; cron job schedule Problem in notation: $(\vec{v}\cdot\vec{\nabla})\vec{v}$ versus $L_v(\vec{v})$ Expanding an event group shows more events than labeled when there are new events I have six upvotes for the one question with no intervening history. They have been summarised into two groups - one with 4 events and one with 2 events. However, when you expand either, both show all 6 events. Minor I know, just letting you know. Why does friction play the role of centripetal force during the turning of a car? How do I disable search-as-you-type text in Ubuntu 17.10 and later? I cannot find enable-interactive-search in    gsettings set org.gnome.nautilus.preferences enable-interactive-search true.     I searched using    gsettings list-recursively | grep search     and    gsettings list-recursively | grep interactive     but no such option.  Can you help me disable this in Ubuntu 17.10 and later? Is the following sentence correct English?      Have you the address?   The address in question is obvious to the person being asked.  It's normal to ask such a question as "Do you have the address?" or even "Have you got the address?" But is it acceptable to use just the verb have without do or got?