Find a sequence of differentiable functions $\{f_n\}$ on $[0,1]$ such that $f_n \to 0$ uniformly, but $\{f_n'(1/2)\}$ does not converge to $0$.   I have tried to find an example which follows above condition, but failed to approach. Please help me!
Give a sequence $(f_n)_{n\in \mathbb{N}}$ of differentiable functions which uniformly converge to $0$, but for which the seqeunce $(f_n')_{n\in \mathbb{N}}$ of the derivatives isn't even pointwise convergent.    I found this one in my textbook marked as "Fun things to solve" and although it may be fun, it's kind of hard to do.   To be honest I already failed at the first hurdle. I couldn't even find a sequence of functions which uniformly converges to $0$.   Is there a certain way of dealing with this kind of problem? Because it seems kind of hard for me to come up with sequences without a mathematical of way of doing so (or maybe there is a mathematical way I just don't know yet).
Is the cube root of a prime number rational? I am using Eclipse 3.3 ("Europa"). Periodically, Eclipse takes an inordinately long time (perhaps forever) to start up. The only thing I can see in the Eclipse log is:       !ENTRY org.eclipse.core.resources 2 10035 2008-10-16 09:47:34.801     !MESSAGE The workspace exited with unsaved changes in the previous session; refreshing workspace to recover changes.   Googling reveals  that I remove the folder:  workspace\.metadata\.plugins\org.eclipse.core.resources\.root\.indexes   This does not appear to have helped.  Short of starting with a new workspace (something which I am not keen to do, as it takes me hours to set up all my projects again properly), is there a way to make Eclipse start up properly? Connecting two relative clauses in one sentence I would like to write an essay which gives information about the charts but because I am not native English speaker, when I started to write down my essay I came across the similar problems that I do sometimes.  Here my sentence:  Figure 1 and figure 2 show the percentage of people, WHOSE age is between 25-44 and over 65, WHO purchased concert, cinema and theater tickets online over the first three months of 2006 in three countries, WHICH are Australia, the UK, Malaysia.  Here is my questions:  1.How can I give the information of age and of what do people buy in one sentence?  2.Such vital and important information on the figures can be used as indefinite relative clause? How to set file input value when dropping file on page? Rotating an object continously with OnMouseDown I have a script that works but it does not do what I want it to do. My script makes an object rotate on when another is clicked. However, I want the object to continuously rotate until I click on the other object again. Right now when I click it rotates just a bit and stops.  Here is my script:   public class Rotate : MonoBehaviour {     public float speed =50f;     public GameObject target;      public void OnMouseDown(){        target.transform.Rotate (new Vector3(0, Time.deltaTime, 0) * speed);     }  }   How can I make the object rotate continuously until I click it again? Format a number with optional decimal places in Excel I have numbers in cells in Excel. I want the numbers formatted so that if they have decimal places they show to a maximum of two, and if they have no decimal places it doesn't show any.  For example.    15 should be formatted as 15, NOT 15.00 14.3453453 should be formatted as 14.35 12.1 should be formatted as 12.1  0 should be formatted as 0   The closest custom format code I've come up with is 0.##. Unfortunately this formats 15.00 as 15. (note the extra decimal point).  To further complicate the issue, the spreadsheet is a result of an export from SQL Server Reporting Services. So no macros are possible. Oh well, it looks like 0.## is my best bet, and they can just live with the extra period. How to easily build your own Linux Distro? I wanted to have a go at creating my very own Linux Distribution. Could you suggest some nice and easy-to-follow tutorials (preferably text based and not videos). I have heard something about Arch Linux but I don't know how to go from there. What do I need? How do I change my Chrome language back to English? I have a daytime raster of my study area. I have 20+ counters in the study area that count "stuff" with a timestamp. Using  I determined the type of ambient light for each collected data point.   What I'd like to do:   Add a grey/semi transparent overlay to reflect the ambient light (Dusk, Sunrise, day, sunset, and dark). The end goal: produce a time-based visualization of the data collection that highlights the time of the day. Or be able to produce a snapshot at a certain time with the proper shaded overlay. Think of this as this the image: Is there a way to detach matplotlib plots so that the computation can continue? After these instructions in the Python interpreter one gets a window with a plot:  from matplotlib.pyplot import * plot([1,2,3]) show() # other code   Unfortunately, I don't know how to continue to interactively explore the figure created by show() while the program does further calculations.  Is it possible at all? Sometimes calculations are long and it would help if they would proceed during examination of intermediate results. Holomorphic self map on the open unit disc Does there exist a holomorphic function $f:\mathbb{D}\longrightarrow\mathbb{D}$ such that $f(1/2)=-1/2$ and $f'(1/4)=1$, where $\mathbb{D}=\{z:|z|&lt;1\}$? Why is quantum entanglement considered to be an active link between particles? From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other.  In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle.  Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred? On SO, when I'm scrolling through "questions" some have a yellow background.  Is this intuitive to everyone but me?  What is the yellow background trying to tell me about this particular question? Windows 10 internet speed capped at half the original speed on new PC What to write in visa application form and what documents to submit as an unregistered freelancer? There are many visa applicants who are working as an unregistered freelancer (photographer, construction contractor, fashion designer, journalist etc ). Some of these freelancers make really handsome monthly income and don't really need to work as a full time employee. Most of them receive variable amount of payments (cash, cheques, demand drafts etc) When it comes to filling a visa application form (USA, UK, Schengen etc), there is always an employment section in all visa form, eg for Schengen visa employment form :    This is a very important factor to make an application really strong.  Questions:   1 Unregistered freelancers can just simply write their profession? what documents to produce along with the application?  2 Bank statements with variable methods of payments could convince the visa officer that these are all legitimate payments? Learning special relativity and working with Minkowski diagrams for a while now i am still trying to get my head around some oddity.   From my understanding time can often be seen as the dependent variable in those diagrams, so why put it to the vertical axis? What confuses me even more is the apparent convention to denote a point in space time $(t,x)$ even though $x$ is on the horizontal and $t$ is on the vertical axis, so the usual notation would be to refer to that vector as $(x, t)$.  Are there mostly historical reasons or why is it beneficial to use this notation and to violate usual conventions? According to the well ordering theorem "". Whenever we have a well ordering on a set, it is not difficult to construct a new well ordering with a largest element. My question is:     For a given infinite set, can we find a well ordering on it such that there is no largest element? How to decide if an effect is magical for Magic Resistance? Some creatures have Magic Resistance:     The [...] has advantage on saving throws against spells and other magical effects.   We know from  that this works against Turn Undead, but does it work against Stunning Strike, Death Strike, Fey Presence, etc? How do we decide? Asymptotic expansion of $u_{n + 1} = \frac12 \arctan(u_n)$ How do I reset my manor so I can rebuild it with different options?