Beginner Exercise 241 / Solution
Black doesn't need to live inside to kill White - only ensure White doesn't have 2 eyes. In this position White cannot make two eyes and so she is unconditionally dead. Thus, Black should tenuki!
Some Example Sequences
Minor point: This is not seki because if Black filled the outside liberties, playing at captures.
This time around, Black prepares to make a rabbitty six in White's eyespace - and it looks like he succeeded. 
 Gronk: Here it is a bit more clearly.