You will be given a trivia clue, and the category it belongs to. You should answer with the best answer that belongs in the category and is described by the clue. For simplicity, answers should be in all lower cased letters.

Category: OPTICS 
Clue: On New Year's or any other day, it's the fineness of detail that can be distinguished in a photographic image
resolution

Category: BON APPETIT 
Clue: From the French for "jump", it means to cook food quickly & lightly in a little butter or oil
sauté

Category: "SHOW" 
Clue: Official nickname of the entity that joined the United States on August 10, 1821

"show-me state"