What does it mean to say that lim n → ∞ an = ∞? the terms an become small as n becomes large. the terms an approach zero as n becomes large. the terms an become large as n becomes large. the terms an become small as n becomes small. the terms an become large as n becomes small?

LET f (x) =, and consider what happens when the values of x become smaller and smaller. Then the values of f (x) become larger and larger. Eventually, they become larger than any number we might name. We then say that the values of f (x) become infinite or tend to infinity, and that the limit of f (x) as x approaches 0 is infinity.

Now, a limit is a number. But infinity, along with its symbol ∞, is not a number and it is not a place. So to "tend to infinity," or to say that "the limit is infinity," is simply the language we use to describe a propertyof a variable; namely that because its values become larger than any number we might name, they do not approach a limit.