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Let $f_n, f \colon [a,b] \to \mathbb{R}.$ Show that, if $f_n \to f$ uniformly, then the Lebesgue integrals are equal, i.e. $\int f = \lim \int f_n$.  This is clearly true for continuous functions, but how do I handle the case of non-continuous functions? I set a command block to /tp. It was supposed to activate only if you had 0 time left, and to activate the command block with a hopper clock to keep giving it power.   But it is not checking if you have 0 time left, so it keeps teleporting me. I can't get close enough to the command block to break it, so I'm stuck in a neverending teleport loop.  Any ideas? Key to get help about current function From my (honestly limited) knowledge of what the Heat Death of the Universe is, I understand that HDotU is the point when energy levels across the entire Universe reach equillibrium, thus energy doesn't flow anymore absolutely anywhere, and thus nothing will ever happen anymore.  If that's the case, would time still be? Even when there's not a single event happening inside it and nobody's there to observe the ticking, does time (or space, come to think of it) exist? Or would HDotU cause something that ends the entire spacetime? zeros of a polynomial Given $P(z)=z^6+6z+10$, find how many roots are in each quadrant    I have already seen that $P(z)$ has six different roots, and that none of them are real or of the form $ki$, $k\in \Bbb R$. Since the coefficients of $P(z)$ are real, then it's roots are 3 conjugate pairs, and therefore the possibilities are limited to two.  Defining $f(z)=z^6$, $g(z)=z^6+6z+10$ and applying Rouche in $|z|&lt;2$, $|f(z)-g(z)|&lt;|f(z)|$ I get that all roots are contained in the disc, but how do I go about splitting them into the four quadrants? From what I know about this polynomial, finding zeros in one quadrant is enough to determine the rest, but I'm stuck trying to apply rouche to a quarter circle (basically I'm having trouble finding a suitable f and g) I am stuck while calculating the peak current in the boost converter through the inductor.  Can you please check if I am right?  Ipeak=(Max Voltage/ R2) = 18/1000=0.018. So, my peak current through the inductor is just 18mA? Am I doing it correct. If this is correct, how will I account for the Vce drop inside the pin1 and pin2 of the IC. The darlington transistor inside the IC is just like a normal transistor. I have added two transistor outside the IC instead of using the darlington switch in the IC for thermal purposes.   Can you please help me with the calculation of Vswce and Ipeak. The calculation of Vswce is not mentioned in the datasheet. So, please help. And the calculation of Peak current is mentioned in the datasheet. But is my approach of calculating the peak current through the inductor right? Correct usage for "all you need is/are..." Okay, obviously beyond Data and the Soong-type androids. But seriously, we have more robots in our daily life now than there apparently are on Trek. Is there a canon answer why not? It seems like Star Wars is more on the nose in this regard - it’s unclear why all dirty/dangerous/boring work wouldn’t be done by robots (anthropomorphic or not). SQL JOIN - WHERE clause vs. ON clause After reading it, this is not a duplicate of . The answer may be related (or even the same) but the question is different.    What is the difference and what should go in each?  If I understand the theory correctly, the query optimizer should be able to use both interchangeably. I am using k-means clustering algorithm to cluster a given dataset into two. I took two different initial points and run k-means clustering algorithm for each initial points. With the first initial points I got “within cluster sum of squared distances” (error) =23874.341. With the second initial points I got “within cluster sum of squared distances” (error) = 42913.684. 23874.341 is less than 42913.684. So, can we say the first one is the better clustering quality? If yes, is it always hold true? Or can we say less within cluster sum of squared distances is always the better clustering quality? What, exactly, is transferred along supply lines? When the good ship Serenity is traveling in deep space, the crew experiences what looks like an Earth-normal (or Earth That Was-normal) level of gravity. Is it ever explained how the ship is able to generate artificial gravity? The ship doesn't spin, so  is out.  is a possibility, but I think the gravity in the ship pulls in a direction that is perpendicular to the direction the ship is usually traveling in, not opposite, like this method would require.   So: how does she pull it off?   Extra credit: how does she pull it off in the episode ? Serenity's engine is totally dead, to the extent where not even life support systems are online. Yet Mal still has to valiantly haul himself around on the floor to replace the compression coil, so whatever creates the artificial gravity on Serenity is clearly still going. How? Is it ever a good idea to close credit cards? I have a bunch of credit cards with no balance, while others have fairly high balances. I'd like to close the 0 balance cards, but I know that will reduce my overall balance and hurt my credit rating, since my ratios of used to unused credit will rise.  Is it ever a good idea to close credit cards? I unintentionally and stupidly wiped my Clash of Clans game data. I went to Application Manager on my Android and clicked 'Clear data'. (I used this for fixes before and it never started a new game.)   Now, my level 60 or so base has been wiped as if was to start a new game. Have I doomed myself to starting again or is there a way in which I can retrieve my old game save? Maybe by contacting Supercell? I have a snapshot of my base. show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$ let $a,b,c&gt;0$. Show that   $$a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$$   By the $$(1+a)(1+b)(1+c)=1+a+b+c+ab+bc+ac+abc$$ it is suffient to show  $$a^2+b^2+c^2+abc+2\ge a+b+c+ab+bc+ac$$ How? How do you fix a bad merge, and replay your good commits onto a fixed merge? I accidentally committed an unwanted file (filename.orig while resolving a merge) to my repository several commits ago, without me noticing it until now. I want to completely delete the file from the repository history.   Is it possible to rewrite the change history such that filename.orig was never added to the repository in the first place? Find all solutions to $x^9 \equiv 25 \pmod {29}$ I don’t like the behavior of the new tab page in Google Chrome 29+. How can I restore the old behavior?  The new tab page (if you have Google set as the default search engine) now shows the Google logo (or, apparently, the doodle of the day if there is one), a search box, and a few recently visited websites. It also added an Apps button to my favorites bar, seemingly the only way to access my apps page, which has easy access to things I use regularly (Calendar, Gmail, Docs, G+, Facebook, Feedly, Google News, Netflix, Play Music, Pandora, Drive, Keep, etc.) I don’t like this behavior. I actually don’t mind having the logo of the day and search box, but I want my apps linked to on my new tab page.  Is there any way to get the old behavior back? I checked the settings and it doesn’t seem like it’s possible to set chrome://apps to be the new tab page (which would restore the old behavior) or to configure the new new tab page to display apps instead of recently visited sites. Intuitive explanation for density of transformed variable? Suppose $X$ is a random variable with pdf $f_X(x)$. Then the random variable $Y=X^2$ has the pdf   $$f_Y(y)=\begin{cases}\frac{1}{2\sqrt{y}}\left(f_X(\sqrt{y})+f_X(-\sqrt{y})\right) &amp; y \ge 0 \\ 0 &amp; y \lt 0\end{cases}$$   I understand the calculus behind this. But I'm trying to think of a way to explain it to someone who doesn't know calculus. In particular, I'm trying to explain why the factor $\frac{1}{\sqrt{y}}$ appears out front. I'll take a stab at it:  Suppose $X$ has a Gaussian distribution. Almost all the weight of its pdf is between the values, say, $-3$ and $3.$ But that maps to 0 to 9 for $Y$. So, the heavy weight in the pdf for $X$ has been extended across a wider range of values in the transformation to $Y$. Thus, for $f_Y(y)$ to be a true pdf the extra heavy weight must be downweighted by the multiplicative factor $\frac{1}{\sqrt{y}}$  How does that sound?  If anyone can provide a better explanation of their own or link to one in a document or textbook I'd greatly appreciate it. I find this variable transformation example in several intro mathematical probability/stats books. But I never find an intuitive explanation with it :( Create a text file using user input from a batch file Is it possible to write a batch file that will create a popup window for the user to input some specific information, and place that information into a text file? The text file should already have some text in it but I just want a couple lines to have input from the user. This is what the text file should look like:  PARTSN="USER INPUT1" PART=blahblah WORKSTATION=blahblah USERID="USER INPUT2" SIZE=blahblah   Where it says "USER INPUT1,2" is where I want the information from the user placed.  Any help would be great!