Are limited common elements at condominium complex considered private?

Your answer depends on what 'private' use you expect of the limited common area that is dedicated to your unit.

Limited common areas are subject to inspection by the association or its agents, maintenance, and insurance, and perhaps more, according to your governing documents.

If you want to film action movies on your deck, store street drugs in your garage or other 'private' acts, be aware that these may be banned, discovered, or disallowed by your association's declarations.

If you want to decorate your private hallway that you share with only two other units of the seventy in your association, your governing documents should be clear on this use.

You are best advised to discuss your 'private' use with your managing agent, or a board member, so that you are confident that your 'privacy' is understood and agreed upon.