Question

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?

Answer 1

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.