wrote:
i would like to cut bean and boomerang shape tables out of 3/4 inch.
plywood.ive been told a router will not do this on one cut with a jig &
using a band saw to smoo9thly cut a continious curve is difficult.any
input on how you would do this would be greatly appreciated.

A router can do it in one cut if you do it this way.

Make a pattern out of hardboard or plywood
Trace onto your 3/4 ply
Cut out freehand on a bandsaw or with jigsaw leaving the line
Attach pattern to your 3/4 using screws or double-stick tape
Use a pattern cutting bit in your router to make the finish cut

OR

Attach pattern to your 3/4 with screws or double-stick tape
Make 3 passes with your router taking ~1/4 at a time
This method requires a thicker pattern