Was taught that showing emotion was a sign of weakness. i have finally found it is not. how do i apologize to exes for being that way?

Sincerely: Make sure that making the apology isn't going to cause harm (like negatively impacting their current relationship). Then hand write a letter or see them in person, maybe over coffee. Email won't cut it if you truly mean to make amends. And this is no time for "cc", "bcc" or posting on facebook. If you want to make it right, do it in person and with feeling.