What are some best practices for handling asynchronous requests and updating page content dynamically in PHP applications using jQuery?

When handling asynchronous requests and updating page content dynamically in PHP applications using jQuery, it is best practice to use AJAX to send requests to the server without reloading the entire page. This allows for a smoother user experience and faster loading times. Additionally, it is important to properly handle the response from the server and update the page content accordingly.

```php
<?php
// PHP code to handle asynchronous request and update page content dynamically

// Check if the request is an AJAX request
if(isset($_SERVER['HTTP_X_REQUESTED_WITH']) && strtolower($_SERVER['HTTP_X_REQUESTED_WITH']) == 'xmlhttprequest') {
    
    // Process the request and generate the response
    $response = array('message' => 'Hello, world!');
    
    // Encode the response as JSON
    $json_response = json_encode($response);
    
    // Send the response back to the client
    echo $json_response;
    exit;
}
?>
```

In this code snippet, we first check if the request is an AJAX request using the `HTTP_X_REQUESTED_WITH` header. We then process the request, generate a response, encode it as JSON, and send it back to the client. This is a basic example of how to handle asynchronous requests in PHP and update page content dynamically using jQuery.