# Limits Involving Infinity

$\lim_{x\rightarrow \infty} \frac{2x + 1}{\sqrt{x^2 - x}}$

In this problem, you're looking at the behavior of the function as x approaches infinity. Limits that involve infinity are unique because infinity is not a number; it represents an idea of something growing without bound. When you take a limit as x goes to infinity, you're asking what happens to the expression as x gets larger and larger, rather than as it approaches a specific value like 0 or 1.

Infinity itself isn't a defined number, but we treat it as a concept that helps us understand how functions behave in extreme cases. For example, while 1 divided by infinity is not actually 0, we say it "approaches" 0 because as the denominator grows infinitely large, the value of the fraction gets smaller and smaller, getting closer to zero without ever truly reaching it. In limits like this one, you're comparing the growth rates of the numerator and the denominator to see how the overall expression behaves as x becomes very large.