Is $i$ equal to $-i$?
Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$ Let $f:(0,\infty) \to R$ be differentiable. Suppose that $\lim_{x\to\infty}(f(x)+f'(x))=L$. Show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$. (Hint: Write $f(x) = e^xf(x)/e^x$ and use l’Hopital’s Rule.)    My working for $\lim_{x\to\infty}f'(x)=0$:  For $\lim_{x\to\infty}f'(x) = 0$, I let $f(x) = e^xf(x)/e^x$ and applied quotient rule which then cancels off $e^{2x}$ and I'm left with $\lim_{x\to\infty}(f(x)+f'(x)-f(x))$. Can I then equate this with $\lim_{x\to\infty} \left(f(x)+f'(x)\right) - \lim_{x\to\infty}f(x)$ which then gives $L-L=0$? Is this step correct? How fast a (relatively) small black hole will consume the Earth? This question appeared quite a time ago and was inspired, of course, by all the fuss around "LHC will destroy the Earth".   Consider a small black hole, that is somehow got inside the Earth. Under "small" I mean small enough to not to destroy Earth instantaneously, but large enough to not to evaporate due to the . I need this because I want the black hole to "consume" the Earth. I think reasonable values for the mass would be $10^{15} - 10^{20}$ kilograms.   Also let us suppose that the black hole is at rest relative to the Earth.  The question is: How can one estimate the speed at which the matter would be consumed by the black hole in this circumstances? I often see questions on Stack Exchange sites which I presume are written by non-native English speakers who use the word "doubt" in place of the word "question". Is this a case of misunderstanding the correct meaning or are people being taught that this is correct usage? load() method deprecated? I  just got these 10 e-mails 5 hours ago from do-not-reply@stackexchange.com:      Recently, you asked a question on [X] Stack Exchange, but you haven't verified your email address yet.      Click on the following link to verify your email and set a password so that you can log in.      Here, [X] refers to all of the following:    GameDevelopment.SE SharePoint.SE Unix.SE  Skeptics.SE Japaneese.SE HomeImprovement.SE SciFi.SE PersonalFinanceMoney.SE  DatabaseAdmins.SE  TeX.SE    I haven't posted on any of these except for TeX.SE, but that was not recently, and through my real account.   =   I asked about this , and was told that someone seems to be impersonating me by using my email. Is it possible for staff to stop this?   Also, I'm pretty surprised there is no measure to stop people from using emails to existing SE accounts (see for example, on wordpress.com, if you use an e-mail which has an existing account on wp.com, you are asked to log in.).    EDIT:  I just got 2 more emails an hour ago for SharePoint.SE, and for AmateurRadio.SE. Learning Resources on Parsers, Interpreters, and Compilers I've been wanting to play around with writing my own language for a while now (ostensibly for the learning experience) and as such need to be relatively grounded in the construction of Parsers, Interpreters, and Compilers. So:   Does anyone know of any good resources on constructing Parsers, Interpreters, and Compilers?   EDIT: I'm not looking for compiler-compilers/parser-compilers such as Lex, Yacc and Bison... How to find the determinant of this $3 \times 3$ Hankel matrix? Today, at my linear algebra exam, there was this question that I couldn't solve.   Prove that $$\det \begin{bmatrix}  n^{2} &amp; (n+1)^{2} &amp;(n+2)^{2} \\  (n+1)^{2} &amp;(n+2)^{2}  &amp; (n+3)^{2}\\  (n+2)^{2} &amp; (n+3)^{2} &amp; (n+4)^{2} \end{bmatrix} = -8$$   Clearly, calculating the determinant, with the matrix as it is, wasn't the right way. The calculations went on and on. But I couldn't think of any other way to solve it. Is there any way to simplify $A$, so as to calculate the determinant? Page Object Model or External property file for Selenium Object Repository I am a beginner in Selenium WebDriver (Java with TestNg). I'm trying to create a framework of my own.  My question here is what would be the better option to store my objects (basically all the webelements of my website under test), Page Object Model or External Property file? Why? Is there a better method than those? Please help. Salesforce1 on focus scroll to the top I have noticed that some browsers (in particular, Firefox and ) are very zealous in using cached copies of .css and .js files, even between browser sessions. This leads to a problem when you update one of these files, but the user's browser keeps on using the cached copy. What is the most elegant way of forcing the user's browser to reload the file when it has changed? Ideally, the solution would not force the browser to reload the file on every visit to the page.  I have found  and  suggestion to be useful. It turns out there is a term for this: auto-versioning. I have posted a new answer below which is a combination of my original solution and John's suggestion. Another idea that was suggested by SCdF would be to append a bogus query string to the file. (Some Python code, to automatically use the timestamp as a bogus query string, was .) However, there is some discussion as to whether or not the browser would cache a file with a query string. (Remember, we want the browser to cache the file and use it on future visits. We only want it to fetch the file again when it has changed.) Why does demand for stock rise when a company appears to have high future value? How to make a Rigid Body fall off a conveyor belt? I've created conveyor belt and and two objects with rigid body physics. But the first object won't fall and second object falls backwards.  How can I fix it? Are there any known uncountable transfinite increasing sequences of real numbers? The real numbers are uncountable, so assuming the axiom of choice there is at least transfinite sequence of real numbers $r_0, r_1, r_2, ..., r_\omega, r_{\omega + 1}, ..., $ up to (and possibly including) $r_{\omega_1}$ that contains an uncountable number of terms. However, it's not guaranteed that $r_0 &lt; r_1 &lt; ..., r_\omega &lt; ...$  Is there a known transfinite sequence of real numbers that is monotonically increasing and which contains uncountably many real numbers?  Thanks! How do I fix Outlook only showing the first line of every message? I'm experiencing a strange problem with Outlook 2019. When viewing a message it only shows the first line. On an HTML message, it stops at the first close paragraph tag. On a plaintext message, it stops at the first newline character. This is true if viewing a message in the reading pane as well as if double-clicking the message to open in its own window. I have the preview pane set to show 3 lines and it does show more of the message so it seems like Outlook can see more of the message than it's rendering in the reading pane. If I use View Source, the underlying data seems fine and the whole message is there. I've tried the following:  Deleting and re-creating the user's mail profile Uninstalling &amp; re-installing Office Creating a new Windows account &amp; connecting Outlook to a different Exchange account than the one that originally exhibited the problem Checked for Windows updates Checked for Office updates  Any ideas what might be causing this? I feel like I've tried everything obvious &amp; I'm striking out on Google. Why: a relative adverb, a conjunction ... or both? I am not familiar with the idea that an adverb can function as a conjunction at the same time. Here are a couple of sentences that are confusing me.     This is the reason why she left him.   ...and     He was transferred to New York, where he was promoted to a higher level.   The  why, where, when, and how seem to introduce a clause. Therefore, can they also be called conjunctions? If yes, would I be right in assuming that relative adverbs can function as conjunctions at the same time? Difference between JOIN and INNER JOIN Both these joins will give me the same results:  SELECT * FROM table JOIN otherTable ON table.ID = otherTable.FK   vs  SELECT * FROM table INNER JOIN otherTable ON table.ID = otherTable.FK   Is there any difference between the statements in performance or otherwise?   Does it differ between different SQL implementations? How to change the order of the subcategory and category in a post? I guess it is something simple which I'm not able to see. Any help would be much appreciated. Best, M. Abnormal PREEMPTIVE_OS_AUTHENTICATIONOPS Waits What regular expression will match valid international phone numbers? Best way to remove an event handler in jQuery? I have an input type="image". This acts like the cell notes in Microsoft Excel. If someone enters a number into the text box that this input-image is paired with, I setup an event handler for the input-image. Then when the user clicks the image, they get a little popup to add some notes to the data.  My problem is that when a user enters a zero into the text box, I need to disable the input-image's event handler. I have tried the following, but to no avail.  $('#myimage').click(function { return false; });