Periodical updating data in separate thread (task actually)

Question

I've been considering what is optimal solution for implementing periodical (relatively long running) computations every x milliseconds in C# (.NET 4).

1. Let say that x is 10000 (10 seconds).

   Probably the best solution in this case is DispatcherTimer which ticks every 10 seconds.
   In void timer_Tick(object sender, EventArgs e) function would be only code which starts Task (lets assume it would take ~5 seconds to complete the long running task).
   timer_Tick would exit immediately and the task would be busy computing something.

2. What about x<1000 (1 second)?

   Wouldn't be there the big performance overhead creating and starting Task every 1 second?
   If not what is the time limit for x? I mean: for some small x values it would be better to start one Task running for all the time until program does not exit. Inside created task there would be DispatcherTimer ticking every x second calling relatively long running function (maybe not 5 seconds but <1 second now; but still relatively long).

   Here comes the technical problem: how can I start the Task which would be running forever (until program is running)? I need nothing but Dispatcher Timer inside of the Task, ticking periodically every x (x is small enough).
   I tried this way:

CancellationTokenSource CancelTokSrc = new CancellationTokenSource(); 
CancellationToken tok = CancelTokSrc.Token;
ConnCheckTask = new Task(() => { MyTaskMethod(tok); }, tok, TaskCreationOptions.LongRunning);

void MyTaskMethod(CancellationToken CancToken)
{
    MyTimer = new DispatcherTimer(); // MyTimer is declared outside this method
    MyTimer.Interval = x;
    MyTimer.Tick += new EventHandler(timer_Tick);
    MyTimer.IsEnabled = true;

    while (true) ; // otherwise task exits and `timer_Tick` will be executed in UI thread
}

---

-- Edit: --

By intensive calculating I meant checking if connection with specified server is up or down. I want to monitor connection in order to alert user when connection goes down.

Checking connection is implemented this way (thanks to Ragnar):

private bool CheckConnection(String URL)
{
    try
    {
        HttpWebRequest request = WebRequest.Create(URL) as HttpWebRequest;
        request.Timeout = 15000;
        request.Credentials = CredentialCache.DefaultNetworkCredentials;
        HttpWebResponse response = request.GetResponse() as HttpWebResponse;

        return response.StatusCode == HttpStatusCode.OK ? true : false;
    }
    catch (Exception e)
    {
        Debug.WriteLine(e.ToString());
        return false;
    }
}