The URL triggering this servlet is "dateAndTime.ajax".
It cannot be handled by the normal JavaServer Faces servlet configured in web.xml:
<servlet>
<servlet-name>Faces Servlet</servlet-name>
<servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
<load-on-startup>1</load-on-startup>
</servlet>
<servlet-mapping>
<servlet-name>Faces Servlet</servlet-name>
<url-pattern>*.faces</url-pattern>
</servlet-mapping>
Instead, we add:
<servlet>
<servlet-name>Ajax Servlet</servlet-name>
<servlet-class>com.corejsf.AjaxServlet</servlet-class>
</servlet>
<servlet-mapping>
<servlet-name>Ajax Servlet</servlet-name>
<url-pattern>*.ajax</url-pattern>
</servlet-mapping>
Here is more information on servlets.