StellarAn infinite limit occurs when the values of a function increase or decrease without bound as x approaches a certain number. Instead of approaching a finite y-value, the outputs grow arbitrarily large positive or negative. This is often written using ∞ or -∞, but these are not real numbers; they describe unbounded behavior. Infinite limits are closely related to vertical asymptotes, because if a function blows up near x=a, then the line x=a is often a vertical asymptote.
When studying infinite limits, it is very important to pay attention to direction. A function may approach ∞ from one side and -∞ from the other. In that case, the one-sided limits are different, and the two-sided limit does not exist in the ordinary sense. So students should not just say “it goes to infinity” without checking left and right behavior carefully. The sign and direction matter.