I have very long trigonometric formulas in latex. I want to print only s instead of printing complete sin in the latex document. same for the cos. Is there any way ?
How can we make First letter Capital while using trigonometric functions. eg: \cos (60^\circ) gives simple cos (all in small). What is needed is 'Cos' (with initial capital). For italics in mactex i used \it but it didn't italicized 'cos' only the number '60'. So how to do that?
0 ram free on ICS How can I make sure that only low and medium security inmates are in a specific area? Is it possible to reverse the overlay you can set? It seems like you are only able to clear areas for low OR medium security prisoners, but sharing is not possible. The thing I want here is to make sure that max security prisoners are not in certain areas. Solving recurrence relation. Recurrence Prove that $\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)&lt;3$   for all positive integers $n$   This problem is copied from Math Olympiad Treasures by Titu Andreescu and Bogdan Enescu.They start by stating that induction wouldn't directly work here since the right hand side stays constant while the left increases.They get rid of this problem by strengthening the hypothesis.$$\left(1+\dfrac{1}{1^3}\right)\left(1+\dfrac{1}{2^3}\right)\cdots\left(1+\dfrac{1}{n^3}\right)\le3-\dfrac{1}{n}$$ and then proceed by induction.  The problem is that I can't find a motivation for the above change.I mean,we could have subtracted a lot of things from the RHS but what should nudge us to try $\dfrac{1}{n}$?The rest of the proof is quite standard,but I can't see how I am supposed to have thought of it.Is it just experience?Or is it a standard technique?A little guidance and motivation will be appreciated. I'm trying to install wifi drivers for a particular mini wifi card i bought. The output of lsusb is:  0bda:f179 Realtek Semiconductor Corp   I've searched everywhere for drivers, but could not find anything. Any help?  Thanks As an example, consider the two sentences:     There don't seem to be any doctors here.   and     There doesn't seem to be any doctors here.   To my ear, the first sounds great, and the second is painfully awkward.  So which is correct, grammatically? I've found lots of disagreement on this around the Web, with various sources citing different ways of treating the word "any" (as singular, always, or as either depending on to what it refers). No consensus, however, could I locate. How to log source file name and line number in Python Reading a Set in PostLoad on JPA/Hibernate Normally, it takes three votes to delete.  It still does, though the mouseover tip for a question with one delete vote cast on it already appears to be stuck at '1'    And then after casting a delete vote on it:    And if I've cast the first delete vote:    The above examples are from P.SE, and while I don't have the privs to verify this being the situation on other sites, this has been confirmed on at least SO and is likely network wide.    Child meta dups:   SO: How to find the real user home directory using python? What does Minecraft's scary music mean? Apparently it means there is a dungeon around but I can never find any?  If it does mean dungeons how far away will it trigger? How do you empty the buffers and cache on a Linux system? Prior to doing some benchmarking work how would one free up the memory (RAM) that the Linux Kernel is consuming for its buffers and cache?    Note that this is mostly useful for benchmarking. Emptying the buffers and cache reduces performance! If you're here because you thought that freeing buffers and cache was a positive thing, go and read . The short story: free memory is unused memory is wasted memory. Logic Behind StackOverflow Question IDs Creating random numbers with no duplicates What is the word for the order of succession in which son assumes the throne after father? It can be any son-younger son after elder son after father. Also, what can be the term for only a single family in power? Please answer. I have a spreadsheet full of addresses to geocode in ArcMap 10.  I've added the spreadsheet to the map, then started to geocode them via the context menu's "Geocode addresses" item.  Many were matched automatically, and most of the unmatched I've been able to resolve within the Interactive Rematch dialog. But I have a handful of addresses where I get no result at all.  I can, however, locate these points on Google Maps, and I can get the latitude and longitude that way.  How can I enter that data into the table to locate the missing points?  I have tried editing the data and putting the lat/lon values into the X and Y columns, (via Edit Features -> Start Editing, then Open Attribute Table on the context menu).  But when I Flash the point, I don't see it.  The lat &amp; lon are consistent with the other data points on the map (i.e., not swapped, and using the correct sign).  How can I add the points to the table? How to pick a specific Pantone color in Photoshop? What about finding a Pantone that is close to a specific CMYK color? How would I select a specific Pantone color in Photoshop, e.g. PMS 5625?  Also, how do you pick a Pantone colour that is similar to a specific CMYK color, e.g. C61, M41, Y58, K16 green?    In this case Pantone 5615C looks closest to the CMYK color. Most OO languages prefix their interface names with a capital I, why does Java not do this?  What was the rationale for not following this convention?  To demonstrate what I mean, if I wanted to have a User interface and a User implementation I'd have two choices in Java:        Class = User, Interface = UserInterface   Class = UserImpl, Interface = User      Where in most languages:     Class = User, Interface = IUser   Now, you might argue that you could always pick a most descriptive name for the user implementation and the problem goes away, but Java's pushing a POJO approach to things and   most IOC containers use DynamicProxies extensively.  These two things together mean that you'll have lots of interfaces with a single POJO implementation.  So, I guess my question boils down to: "Is it worth following the broader Interface naming convention especially in light of where Java Frameworks seem to be heading?" Illustrator Vector Graphics Appearing Pixellated This has been puzzling me for a few days now, and I asked a graphic designer I knew before trying here and haven't been able to solve it yet. It's quite weird so please bear with me for a bit.  I am using Adobe Illustrator to create a logo, and I have something that can potentially work. I have used only the pen tool with strokes (no fill), but the issue is, when I view the logo at 100%, it looks pixellated! I know vectors should not even be able to appear pixellated, but they are. Here is the screenshot from AI, without exporting to anything:     That was just done using the snipping tool within Windows, and it's at 100% zoom.  I have anti-aliasing turned on from Edit > Preferences > General, and the document resolution is at 300 ppi (I get the same result with 72 ppi).   Could anyone help me with this?   If relevant: Using CS6, and have a 24 inch Dell U2412M at 1920x1200 resolution. I do have a 21.6" Samsung at 1680x1050 and I get the same result there as well. Let me know if you need any other settings, or if you would like the file, I'd be happy to provide it to be able to solve this problem. Using R, I have fitted a linear model for a single response variable from a mix of continuous and discrete predictors. This is uber-basic, but I'm having trouble grasping how a coefficient for a discrete factor works.   Concept: Obviously, the coefficient of the continuous variable 'x' is applied in the form y = coefx(varx) + intercept but how does that work for a factor z if the factor is non-numeric? y = coefx(varx) + coefz(factorz???) + intercept   Specific: I have fitted a model in R as lm(log(c) ~ log(d) + h + a + f + h:a) where h and f are discrete, non-numeric factors. The coefficients are:  Coefficients:               Estimate  (Intercept)  -0.679695  log(d)        1.791294  h1            0.870735   h2           -0.447570   h3            0.542033    a             0.037362   f1           -0.588362   f2            0.816825  f3            0.534440 h1:a         -0.085658 h2:a         -0.034970  h3:a         -0.040637   How do I use these to create the predictive equation:  log(c) =  1.791294(log(d)) + 0.037362(a) + h??? + f???? + h:a???? + -0.679695   Or am I doing it wrong?   I THINK that that concept is if the subject falls in category h1 and f2, the equation becomes:   log(c) =  1.791294(log(d)) + 0.037362(a) +  0.870735  + 0.816825  + h:a???? + -0.679695   But I'm really not clear on how the h:a interactive term gets parsed. Thanks for going easy on me.