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Task manager for Ubuntu How do I get a bigger static scrollbar (aka normal scrollbar)? What is the difference between a gameplay programmer and a game designer/developer? Check if a services is installed using C Can all real polynomials be factored into quadratic and linear factors? So I understand how to do integration on rational functions with a linear and a quadratic denominator, and I understand how to do a partial fraction decomposition, but I was wondering what happens if the polynomial is higher degree and can't be factored. Later in the page, it says this:     However, it can be shown that any polynomial with real coefficients is a product of linear and/or irreducible quadratic factors with real coefficients.   And I was wondering, how do we know this and is this definitely true? Why is sample standard deviation a biased estimator of $\sigma$? 1N5819-E3/73  1N5819-E3/53 1N5819-E3/54   the first one is 4x cheaper than the last, why ?  aren't they all the same ? Can US stocks list on one stock exchange but trade on other US stock exchanges? I am trying to understand how the US stock market works. From my understanding, there is one stock exchange where a company is &quot;listed&quot;. This stock exchange listing requires the company to adhere to the regulations of the stock exchange where it is listed. Once a company is &quot;listed&quot;, its shares can start to trade on any stock exchange. For example, once a company lists on NASDAQ, its shares can be traded on NASDAQ, NYSE, Boston Stock Exchange, Philadelphia Stock Exchange, National Stock Exchange, EDGX Exchange, EDGA Exchange, NYSE Arca, etc. Is my understanding correct? Is it true that once a stock is listed on a US stock exchange, the stock can then trade on any US stock exchange? Consider the Level 2 quotes for Microsoft (NASDAQ: MSFT). Microsoft is only listed on NASDAQ, but it also trades on the NYSE and other stock exchanges:  My questions are:  Does this mean that companies only need to be listed on one stock exchange in order for their stock to trade on other stock exchanges?  If so, do companies need to adhere to the &quot;listing requirements&quot; of all the stock exchanges where their stock is traded, even though they are not &quot;listed&quot; on those stock exchanges? Does Microsoft have to follow the listing requirements of the NYSE even though it is not listed there?  If stocks can trade on any US stock exchange regardless of which US stock exchange the stock is listed on, why don't NYSE-listed companies reduce their yearly listing fees by listing on NASDAQ instead? Finding the limit of $(1-\cos x)/x^2$ $$\lim _{x \to 0}{1-\cos x\over x^2}={2\sin^2\left(\frac{x}{2}\right)\over x^2}={\frac{2}{x^2}\cdot {\sin^2\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)^2}}\cdot\left(\frac{x}{2}\right)^2$$  now $$\lim_{x \to 0}{\sin^2\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)^2}=\left({\sin\left(\frac{x}{2}\right)\over \left(\frac{x}{2}\right)}\right)^2=1^2$$  So we have $$\frac{2}{x^2}\cdot \left(\frac{x}{2}\right)^2=\frac{2}{x^2}\cdot \left(\frac{x^2}{4}\right)=\frac{1}{2}$$  Are the moves right? Title, section headings disappears when I use \usepackage{forest} with IEEE Access template When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? In the PGF/TikZ manual, sometimes I see the option right of=somenode instead of right=of somenode. They look very similar, but the effects are different.  The distance between nodes positioned with the latter option is boundary-to-boundary, as stated in the manual. However, with the first option, it seems that the distance is shorter. I couldn't find any explanation of the first option in the manual.  My question is: what is the difference between the two options? Is there any explanation in the manual that I missed? How to use early stopping properly for training deep neural network? Can I look at the upgrade log after a distribution upgrade? I've upgraded to Ubuntu 12.04 and did it . I didn't look at the "packages to remove" section before clicking next - I've done Ubuntu upgrades many times and assumed it was just the normal set of obsolete library packages etc. But I do tend to watch the terminal text go by and see what it's doing, and I saw it removing a number of packages I wanted. I guess these are packages that aren't on the CD that can't co-exist with the new Ubuntu.  Anyway, I want to find which packages have been removed. So does the update log get saved somewhere?  Then I can start doing some grepping on it and then reinstall the packages I did want. Query to list number of records in each table in a database How to search entire hard drive for a file? How do I set the proper exposure for nighttime moon photos? All my attempts to get a good shot of the full moon with my DSLR result in an overexposed circle on a black background.  I've tried using a tripod, remote shutter release, low ISO, and long exposure, but nothing has worked so far.  What combination of ISO and exposure time that will produce good results?   I particularly want to catch a full moon with the reddish effect when it is close to the horizon. If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$ If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$. Here is my attempt at a proof. It feels very elaborate and I am not sure if it is correct. Can someone please point out any mistakes or places where I may improve. Thanks!  By the definition of continuity at $a$ of $f,g$ we have that $\lim\limits_{x\to a}f(x)=f(a)$ and $\lim\limits_{x\to a}g(x)=g(a)$. Suppose that $f(a)&gt;g(a)$. Then there exists a $\delta&gt;0$ such that $f&gt;g$ for all $x$ satisfying $|x-a|&lt;\delta$. Then for $x$ satisfying $|x-a|&lt;\delta$ we have $h(x)=f(x)$ and $k(x)=g(x)$ and thus $h$ and $k$ are continuous at $a$ because $f$ and $g$ are continuous at $a$. Now if $f(a)&lt;g(a)$ we simply relabel $f=\tilde{g}$ and $g=\tilde{f}$, so that $\tilde{f}(a)&gt;\tilde{g}(a)$ and we apply the previous result to show that again $h$ and $k$ are continuous at $a$.\  Now if $f(a)=g(a)$ then we can distinguish three cases. $f\geq g$ in a small neighborhood about $a$, $f\leq g$  in a small neighborhood about $a$ or $f\geq g$ on one side of $a$ and $f\leq g$ on the other side. In the first case we assume that $f\geq g$ in some small neighborhood about $a$. Then, since $f(a)=g(a)$ we have $h(x) = f(x)$ in this neighborhood and $k(x) = g(x)$ and again we see that $h$ and $k$ are continuous at $a$ due to the continuity of $f$ and $g$ at $a$. Similarly if $f\leq g$ in a neighborhood around $a$ then $h(x)=g(x)$ and $k(x)=f(x)$ in this neighborhood and $h$ and $k$ are continuous at $a$.   Suppose that just to the left of $a$ we have $f\geq g$ and just to the right of $a$ we have $f\leq g$. Then $\lim\limits_{x\to a^-}h(x)=\lim\limits_{x\to a^-}f(x)=f(a)=h(a)=g(a)=\lim\limits_{x\to a^+}g(x)=\lim\limits_{x\to a^+}h(x)$. Similarly $\lim\limits_{x\to a^-}k(x)=\lim\limits_{x\to a^-}g(x)=g(a)=k(a)=f(a)=\lim\limits_{x\to a^+}f(x)=\lim\limits_{x\to a^+}k(x)$. So $\lim\limits_{x\to a}h(x)=h(a)$ and $\lim\limits_{x\to a}k(x)=k(a)$ which means that $h$ and $k$ are continuous at $a$. Lastly if $f\leq g$ just to the left of $a$ and $f\geq g$ just to the right of $a$ we can relabel $f=\tilde{g}$ and $g=\tilde{f}$ and apply the last result to show $h$ and $k$ are continuous at $a$.   Again, please point out any mistakes I may have made. Thanks!! Is Pikachu's gender ever confirmed? I was recently having a discussion about Pokémon, and it came up that none of us were sure whether Ash's Pikachu in the series was male or female. Some (myself included) always thought it was male, whereas others could've sworn it was female.  Was there ever any canon evidence to point in one direction or another? Gaps between arrows and labels Are there any synonyms for the noun 'crush'? I must clarify, when I say 'crush', I mean the subject of an unrealistic, one-sided infatuation. For example, it can be used in this sentence: 'My celebrity crush is David Beckham.'  Could that word be interchanged for another? Preferably, can it be a word which is not necessarily too formal/complex? I've searched online for a while but can't find any synonyms for this form of 'crush.'  I want the word for a novel which is set in an old-ish fantasy period so I don't think 'crush' would feel in-place.  The main character is a lower-class worker.