original_query: What is the definition of the limit of a function as x approaches infinity?
query: What is the definition of the limit of a function as x approaches infinity?
answer: The limit of f(x) as x approaches infinity is L, denoted lim_(x→∞) f(x) = L, means that for all ε > 0, there exists a c such that |f(x) - L| < ε whenever x > c.  Similarly, the limit as x approaches negative infinity is defined.