We are now oscillating around the horizontal asymptote. And once again, this limit can exist. Even though we keep crossing the horizontal asymptote, we're getting closer and closer and closer to it the larger x gets. And that's actually a key difference between a horizontal and a vertical asymptote. Vertical asymptotes, if you're dealing with a function, you're not going to cross it. While with a horizontal asymptote, you could. And you are just getting closer and closer and closer to it as x goes to positive infinity or as x goes to negative infinity.