Prove that $\lim_{x \to 0} \frac{f(x)}{x}=0$
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
Top of answer covered by sticky top bar after clicking direct link Number of finite simple groups of given order is at most $2$ - is a classification-free proof possible? SFDX Pull fails because of AppMenu/AppSwitcher The set of homotopy classes Outline around text on CMYK black background in Photoshop I'm trying to make a document with one color black  (c:0,m:0,y:0,k:100) background with red text on it. However in CMYK the text has this weird grey white-ish edge. In RGB it doesn't show but in CMYK it shows. I'm wondering will this show when printing or do I need to use different methods? ie. using rich black etc.  Here's the RGB and CMYK comparison If $A^2\succ B^2$, then necessarily $A\succ B$ I remember reading somewhere about the following properties of non-negative definite matrix. But I don't know how to prove it now.  Let $A$ and $B$ be two non-negative definite matrices. If $A^2\succ B^2$, then it necessarily follows that $A\succ B$, but $A\succ B$ doesn't necessarily leads to $A^2\succ B^2$.  How can you prove it? Thanks! Can an electron be in two places at the same time? So I've been reading a bit and watching some videos about the double slit experiment, and therefore the wave particle duality; I've also read this "implies" that a particle can be in two places at the same time. Can you clarify this, and how could that be possible? Rigid body simulation not interacting with objects that have an array modifier Position vs Part Java: Difference between the setPreferredSize() and setSize() methods in components How to install the most common plugins? Functions Which are non differentiable on a Given Set. My roommate put a hunk of beef roast in the slow-cooker for a good 6 hours.  It's a fairly large sized slow-cooker, at least 8 quarts.  The meat was cooked through but very chewy, and I never remember my mom having that issue with a slow-cooker.  My roommate tends to put only enough water to get halfway up the side of the roast, and always uses a slow-cooker 'bag' (another thing my mom never did).  What advice can I offer them to get a better outcome? Compute Engine - 1000 GB disk cant decrease size i have a huuuuge problem.  Created a snapshot and image from my instance...instance has 1000GB of disk.  Now i need to reduce it but everytime i try to create an image or a snapshot from that, i get the same error "Disk need to be at least 1000GB".  There is a way to reduce disk size directly on instance? Some workaround? Exit of "> " mode in Unix shell In sh (not Bash), how would we abort execution of command when the prompt is in &gt; mode?  For example, when entering a string with quotes only at the beginning, it makes the prompt look like &gt;, without the ability to quit it normally, unless hitting Ctrl + D. Example:  root@MyPC:~# echo "hello &gt; I am &gt; (How do I exit of this mode?)   In case that I don't know which character delimits the string (" or ' or simply escaping a newline/spaces with backslash), is there a way to let Bash know that I want to abort the execution of the current command? Where are static variables stored in C and C++? Simultaneous collaborative editing of a LaTeX file Sending Email via gmail smtp server in JAVA I have a circuit board in production, primarily through-hole, to the tune of ~400 units per year. Each one is manually inspected and tested. The board has ten distinct voltage rails, four voltage feedback amps, three current feedback amps, a microprocessor with particular response characteristics, and a few other parts. That's a lot to check.  I'm considering building an automated test rig for all that. I think a PCB that feeds the appropriate input stimuli, observes the responses, and gives a go/no-go would save me a lot of time. I'm reasonably confident that this is done, commonly. However, the techniques used to do it are unknown to me.  I imagine a test rig with a circuit board of the same footprint as the unit under test (UUT). It would have a microprocessor, appropriate protection and scaling circuitry, and a large number of vertical pins sticking up from the board. Mount points would also stick up from the test rig for the UUT. When the UUT is mounted on top of the test rig, the bottom of the board makes contact with the vertical pins, allowing the test rig to feed stimuli to the UUT and observe responses.  This seems reasonable, and I have the idea I've seen something very much like this before. But the details elude me. What sorts of pins would be used on the bottom board? (Part numbers would be great!) Would I need to put specific kinds of test points on the UUT, or can I get away with just contacting the clipped pins protruding through the board? What other concerns might there be? When is it ok to remove the intercept in a linear regression model?