Concept preview

What you will be able to do

1. 01Interpret $\lim_{x\to c} f(x)=+\infty$ or $-\infty$ as unbounded one- or two-sided behaviour, and state clearly that such a limit means the finite two-sided limit does NOT exist.
2. 02Locate a vertical asymptote of a rational function as an $x$-value where the denominator approaches $0$ while the numerator stays nonzero, and distinguish it from a removable hole.
3. 03Determine the sign ($+\infty$ vs $-\infty$) of each one-sided infinite limit by tracking the sign of the numerator and denominator as $x$ approaches the asymptote.

So far in this unit you have evaluated limits that settle down to a single finite number. But some functions do the opposite near certain points: instead of settling, their outputs race off toward $+\infty$ or $-\infty$. This lesson (AP topic 1.14) is about those runaway situations, called infinite limits, and about the vertical asymptotes they create on a graph. Learning to read them turns a confusing spike on a graph into a precise, predictable statement about behaviour.