As a general rule, when you are taking a limit and the denominator equals zero, the limit will go to infinity or negative infinity (depending on the sign of the function).

How do you prove a limit equals infinity?

In proving a limit goes to infinity when x x x approaches x 0 x_0 x0​, the ε \varepsilon ε- δ \delta δ definition is not needed. Rather, we need only show that the function becomes arbitrarily large at values close to x 0 .

What is meant by infinite limit?

A limit in which f(x) increases or decreases without bound as the value of x approaches an arbitrary number c is called an infinite limit. This does not mean that a limit exists or that ∞ is a number. In fact the limit does not exist.