Explain briefly the function of the code below. About continue &amp; break operations. I can't understand properly label1, label2.....Please describe code functions   (The label is basically used in nested loops  But note that they are used here to understand the labelling process)  class example {     public static void main(String args[]) {         int i = 0;         int j = 0;         label1: while (i++ &lt; 5) {             label2: for (;;) {                 label3: do {                     System.out.print(i + " " + j + " ");                     switch (i + j++) {                     case 0:                         continue label3;                     case 1:                         continue label2;                     case 2:                         continue label1;                     case 3:                         break;                     case 4:                         break label3;                     case 5:                         break label2;                     case 6:                         break label1;                     default:                         break label1;                     }                 } while (++j &lt; 5);             }         }     } }
I saw this keyword for the first time and I was wondering if someone could explain to me what it does.   What is the continue keyword? How does it work? When is it used?
I've seen $d(xy) = y(dx) + x(dy)$, but I don't understand the principle behind it and memorizing it is lame.  Can anyone explain what is going on here?  For example from physics, $$F = {{dP} \over {dt}}$$ $$F = {{d(mv)} \over {dt}}$$ $$F = {{v(dm) + m(dv)} \over {dt}}$$ Since $$dm = 0$$  $$F = {{m(dv)} \over {dt}}$$ Since $$a = {{dv} \over {dt}}$$ $$F = ma$$ How can I rewire half switched receptacles? In my bedroom the bottom half of all receptacles are controlled by one switch. Is it possible to have just one receptacle with top and bottom hot all the time?  The top half is hot all the time the bottom half is controlled by one switch.  Keep in mind there are six other receptacles in this room that are the same way controlled by the same switch. When I took the receptacle out the right side tab had been removed.  The top right screw had a black wire, the bottom right had a red wire, the top and bottom left screws had separate white wires.  I changed the receptacle out as suggested, I capped off the red wire and I capped off the white wire that was attached to the bottom left screw. I attached the other white wire to the top left screw and attached the black wire to the top right screw. I now have none of the receptacles working at all. What did I do wrong? Evaluate  $$\int\frac{e^xdx}{(e^{2x}-1)(e^x+1)}$$  I tried to decompose the integrand into A and B partial fractions.  No success. I am trying to solve a 2 part question, the first part is to expand $\sqrt{1-x}$ up to and including the term $x^2$ which I did.  This gives me $1-(0.5)x-(0.125)x^2 + ...$  However, the 2nd part of the question says that by taking $x=(1/64)$ in the expansion of part (i) -> which refers to the one above, deduce that $\sqrt 7 = 10837/4096$. How do i do this part?  EDIT (After Hint Given By SimpliFire):  $$ \sqrt{1-\frac1{64}}=\frac{\sqrt{63}}8=\frac38\sqrt7 $$ $$ =\frac83\sqrt{1-\frac1{64}}\;=\sqrt7 $$ $$ =\frac83\left(1-\frac12\left(\frac1{64}\right)-\frac18\left(\frac1{64}\right)^2\right)\; $$ $$ =\frac83\left(1-\frac1{128}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32768}{32768}-\frac{256}{32768}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32511}{32768}\right)\; $$ $$ =\frac{260088}{98304} $$ $$ \frac{10837}{4096}\;\approx\sqrt7 $$  I'm not sure if I can present it like this, if it is okay i will post it as my answer :X Stance on repost question instead of editing to invalidate answers? Finding distance between points in two different layers along route in ArcMap? I need to find the distance between points in separate layers along a stream network. I have source sites for macro-invertebrates and sites where they are lacking. 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I noticed that Amazon does this as well, for example:  &lt;script type='text/javascript'&gt;   if (typeof window['jQuery'] == 'undefined') document.write('&lt;scr'+'ipt type="text/javascript" src="http://z-ecx.images-amazon.com/images/G/01/javascripts/lib/jquery/jquery-1.2.6.pack._V265113567_.js"&gt;&lt;/sc'+'ript&gt;'); &lt;/script&gt; LED light needs replacing every few weeks I have two GU5.3 bulbs in my bathroom - one of them went off a month or so ago so I bought the following 3 pack:   I've gone through 2 of the new bulbs in the space of weeks. I have never seen the bulbs fade out while being on, it's only when we turn the light switch on that they don't come back on (like this morning, I was first in the bathroom and the bulb was off again). No fuses blown or any indication of tripping.  How should I approach this? Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible