"Go out on a limb" means that you do something risky for someone else. (Going on a narrow limb on a tree).
"Play by ear" means you improvise as you go. (Playing an instrument after hearing a song immediately).
"Teaching an old dog new tricks" means sometimes it's hard to teach someone something new if they become set in stone about something. (After a dog has passed a certain age it may be harder to teach it tricks).
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