Anything that you'd use in an informal communication is inappropriate for a business letter. This includes slang, text_speak, emojis, and anything off_color or casual. If you're used to communicating mostly with friends, family, or even co_workers you've worked with for a long time, an appropriate closing for a business letter will probably feel pretty stilted at first. Don't worry about it – your colleague or business associate won't feel that way when he or she reads your correspondence. What seems unnatural to you will feel respectful and polite to the recipient.
For instance, in a typical job application, the problem is that the company or organization needs a position filled, and more importantly they need someone who can do the job well and help the organization achieve its mission (which may be more profits, or it may be to save children in Darfur or to end global warming or to cure cancer). You arouse their interest by telling them that you’re the right person for the position and by promising to help them achieve their mission.