AJAX is most useful when your application wants to present a dataset for its user in many ways. Sorting and filtering and, in general, interacting with a dataset is best when there are no delays waiting for the server to redraw the pages and send them over the network. This is also good for processing the display of new data coming to the server - the client can simply pull out the new data and combine it into a data set on the client, and not require a whole new draw, including all the data that you have seen before. This can save quite a bit of bandwidth.
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