abajpai wrote:

Is it ok to open a connection to the database, do the necessary work, and then close the connection each time a servlet (controller) is called? or is it preferred to open a connection in the initial servlet and leave it open endlessly?

Yes.

or is it preferred to open a connection in the initial servlet and leave it open endlessly?

Don't do this. It's bad programming practice, and it may actually lead to worse performance because then all requests have to wait for the same connection.

Another question regarding database connections. 

To open a connection with the database, the code needs to be surrounded by a try/catch block. After the connection is established, should the necessary work to be done with the database be done inside try block as well or out side it? I think it works either ways if the connection succeeds, and if that is the case, which one is more efficient?

You're right. Thanks professor.