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Add some println() statements to those methods and do some experiments to see when they are called.

Sorry, I don't know anything about jQuery and very little about javascript.

I don't understand what that means. What does "prints on the jsp" mean? Is that a way of saying that the servlet creates an HTML page to return using the jsp code?

I thought every new HTML page...

Can you trace the sequence of events with a bit more detail?
For example:
The browser loads an HTML page from a server at a URL
The user presses some button
The browser sends a request to the...