What is a limit?

Question

Mathematical analysis

There is no idea what lim is, what it calculates and for what? I watched several videos from YouTube, but did not catch up. If possible, explain in simple language, without complex mathematical terms or on real objects (as for children - "2 apples, cut in half = 4)"

Answer 1

Well - there are some numbers we can't reach. For example, an infinitely large number.
If you find such - I will add to it - say, even - one - and we will get a larger number. Therefore, we designate it as a limit - infinity.
And now for example - take your apple. Let's agree that we are not limited by physical limitations.
And divide it into an infinite number of pieces. What will be the size of one piece? An infinitely small value, but not zero, since we can divide any arbitrarily small piece into two more - and so on ad infinitum. In this case, our limit will tend to zero, but not reach it.

Answer 2

As I understand it: A limit is some value that a variable tends to but cannot reach.
For example, in your example, the function is "the number of halves of an apple", where the number of apples is x
f (x) = x * 2
When x tends to infinity, f (x) will also tend to infinity.
Or a more telling example:
f(x) = 1/x
As x tends to 0, f(x) will tend to infinity.
It is written something like this:
lim(x->0; f(x))=∞

Answer 3

My favorite: the limit is the point.
The whole point of the theory of limits is precisely in

complex mathematical terms

Answer 4

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Answer 5

Most likely an error in the request, namely here:
$query = "INSERT INTO myotziv(title, date, time, text ) VALUES ('$name', '$date', '$time', $text')";
treated like this:
checked like this:
PS
generate date and time on the server when receiving data and check if there was a POST on

if($_SERVER['REQUEST_METHOD'] == POST){
    //Дальнейшие проверки
}

update:
$query = "INSERT INTO myotziv(title,date, time, text) VALUES ('$name', '$date', '$time', $text' )";
missing single opening quote