Develop Reference

How find square root n by computing the next Xi term on javascript

Write the function sqrt(A) for computing square root of positive real numbers using next numerical method xi+1 = (1/2) * (xi +(A/xi)). Where the A - input rial number;
On zero iteration next statements have been taken: x0 = A;
The error should be at least 10^-6

You could take the last value xi-1 and compare it with the new value xi instead of using a loop counter.
function sqrt(a, x = 1) { // take 1 for x(0) as start value for recursion
var y = (x + a / x) / 2; // prepare next value x(i+1)
if (x === y) { // exit condition
return x;
}
return sqrt(a, y); // tail call optimization
} // https://stackoverflow.com/q/310974/1447675
console.log(sqrt(2));
console.log(sqrt(10));
console.log(sqrt(9));
console.log(sqrt(25));

Looks like your requirement is not just finding the square root of a number. If by any chance that is your requirement, use Math.sqrt.
If your requirement is to implement a function to find the square root for educational purpose, what you need is to write a recursive function as below. Modify the code as required to support error at 10^-6
function sqrt(A, i = 0) {
if (i === 0)
return A;
let prev = sqrt(A, i - 1);
return 0.5 * (prev + (A / prev));
}
console.log(sqrt(2,1000));
console.log(sqrt(3,1000));
console.log(sqrt(9,1000));
console.log(sqrt(25,1000));

Using f(x) = 1/x in JavaScript

Every millisecond, variable light is incremented by one until it reaches 1/3rd of variable universe, or until it's 3 times the variable matter.
if (light < (universe * (1/3)) || light < matter * 3 && light <= universe) {
light++;
}
Instead, I want light to increase slower the closer it gets to the top,
(1/3rd universe or 3 * matter)
like this picture ( f(x) = 1/x ).
How do I do this?

Something like this might work:
var speed = 10;
var target = Math.max(universe / 3, Math.min(universe, matter * 3));
if (light < target) {
light += (target - light) / speed;
}

You need to make sure that light is a floating point variable, the ++ operator would usually used just for integers.
You just need to add on 1/light on each iteration
-
var light = 0.0;
if (...) {
light += 1/light;
}

So here speed starts out by 100, and then i added a interval so it continues every 1000milliseconds/1second and it will go on.
(function(){
setInterval(function(){
var speed= 99999999;
if(light<(universe/3) || light<(matter*3) && light <= universe)){
light+=speed;
speed--;
}
},1000)
})()
And Yes.. Infinty is a keyword in javascript.

Looped algorithm to increment a number until it reaches a value, then decrement

I'm trying to increment a number until it reaches a value (say 100), then make it decrement until it reaches 0, and have all this run in a while loop.
The code seems correct, but the browser is freezing, so I can't check in the console if there's a flaw in the algorithm.
var ceiling = 100;
var floor = 1;
var x = 1;
var step = 1;
setInterval(function(){
while(1) {
while(x + step <= ceiling) {
x += step;
document.write(x + ' ');
}
while(x - step >= floor) {
x -= step;
document.write(x + ' ');
}
}
}, 1500);
I've used setInterval here to slow down execution and avoid some buffering issue with the browser. It shouldn't be a problem since I have 16GB of RAM, but it might depend on how the browser can use/access that too in one tab.
I've also tried wrapping the setInterval function inside another function and execute it, with the same result.

You have a while(1) loop which basically is a infinite loop, even if no code is executed, it will freeze the browser.

The other answers have already pointed out the problems with your endless loop and with using document.write.
I think this does what you want:
var ceiling = 100;
var floor = 1;
var x = 1;
var step = 1;
setInterval(function() {
console.log(x);
x += step;
if (x === ceiling || x === floor) {
step = -step;
}
}, 1500);
setInterval is essentially your while(1) loop.

document.write is only intended to be used on the first rendering of the document. since you are doing an interval, then the doc is already rendered, and you can't use document.write. instead, you need to append your text to the body or a div

If function javascript not working

I'm a total javascript noob and I'm just trying to bludgeon my way through this simple project. Whats supposed to happen is the script is only meant to run while y <= 3. Each time that it runs the second IF statement, it's meant to add one to y's count and if it runs the ELIF, it's meant to subtract one from y's count. The goal is so that you can only have 3 "selected" pictures at any one time. My y does definitely change, but the IF (y <= 3) does not seem to stop the program from running. Thanks in advance, Jack
<SCRIPT type="text/javascript">
var y = 4; //this is a counter
function swapRoast() { //This defines the function
var x=document.images; //this automatically creates an array of all the images in the document starting with image0 and assigns them to variable'x'
if (y <= 3); { //this should check that y <= 3 before running
if (x[0].src.match('Roast_Vegetables.png')) //This tests if the source of image0 in the array matches the script
{
x[0].src=('Roast_Vegetables_Selected.png'); //If the source matches, then it is changed
y ++; //should add 1 to the y count
}
else if (x[0].src.match('Roast_Vegetables_Selected.png')) //If the source doesn't match, then it tests a different source
{
x[0].src=('Roast_Vegetables.png'); //If the different source matches, then the script operates in reverse to the original IF
y --; //should subtract 1 from the y count
}
}
}
function swapVege(obj) {
var x=document.images;
if (y <= 3); {
if (x[1].src.match('Vegetables.png'))
{
x[1].src=('Vegetables_Selected.png');
y ++;
document.getElementById("demo").innerHTML = y;
}
else if (x[1].src.match('Vegetables_Selected.png'))
{
x[1].src=('Vegetables.png');
y --;
document.getElementById("demo").innerHTML = y;
}
}
}

The semicolon is unfortunate and terminates the if block immediately. Change (in both places)
if (y <= 3); {
to something like
if (y <= 3) {

if (y <= 3); {
take out the ";" here

Javascript animate math

I'm struggling to get my head around such simple Math, well at least it seems it should be simple.
I'm basically trying to mirror what jQuery's .animate does, but to no luck.
Here's a simplified version of what I have so far:
var args = {
speed: 1000, // 1 second.
left: 65 // distance.
}, rot, step;
// Terrible math.
rot = step = (((args.left / args.speed) * 10) - 0.10);
var t = setInterval(function() {
if(elem.style.left >= args.left) {
clearInterval(t);
return;
}
rot += step;
elem.style.left = rot;
}, 10);
Please excuse any illogical code (or math), I've been messing around for a good few hours and totally lost my sanity.

Edit:
Here's the way I would do it.
var start_time = Date.now();
// Get the starting time in milliseconds
var t = setInterval(function() {
var delta_time = Date.now() - start_time;
// Get time that has elapsed since starting
if (delta_time >= 1000) {
// if it's been a second
clearInterval(t);
// Stop the timer
elem.style.left = args.left + 'px';
// Set the element to exactly the value it should be (avoids having it set to a float value)
return;
}
elem.style.left = delta_time * args.left / args.speed + 'px';
// Move the element according to how much time has elapsed
}, 10);​
This method has a few advantages. For example, you can adjust the interval to make it more or less smooth, and it won't mess up the animation.
The reason why your solution was taking longer than one second is because of how you used setInterval. setInterval doesn't account for the time your code takes to run, so the total time is always increased by a bit. You can fix this by using delta timing (like in my example).

Try using useing sin and cos to calculate rotation Some what like this
newx = distance * Math.cos(direction) + x
newy = distance * Math.sin(direction) + y
Not sure , this will solve your problem I guess you want to to do a smooth rotation
Try making it as a function it will work , I am not seeing any problem in your math ,
like this
function move(elem) {
var left = 0
function frame() {
left++ // update parameters
elem.style.left = left // show frame
if (left == 100) // check finish condition
clearInterval(id)
}
var id = setInterval(frame, 10) // draw every 10ms
}

Well for one it should be
var args = { ... }
assuming you have the elem set up correctly, you're going to need a inline styling of the attribute you want to animate. Also, you're going to need to parse the style since it has the 'px' attached to it, but you can always add that after you do the math within the interval function.
I set up something here so you can mess around with the settings and whatnot.
edit:
http://jsfiddle.net/mb4JA/2/
edit2:
this should be one second
http://jsfiddle.net/mb4JA/4/
final answer ;) http://jsfiddle.net/mb4JA/10/
You should be able to put any speed in there, and have it animate for that amount of seconds.