In Precalculus infinite limits describe what a rational graph does next to a vertical asymptote. Substitute first: a nonzero number over zero means the limit is infinite, and the signs on each side decide whether it is ∞ or -∞.
Also taught in Calculus, at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
Substituting gives -2/0, so the limit is infinite, not a number.
The bottom is squared, so it is a tiny positive number on both sides of -3.
A negative top over a tiny positive bottom runs down on both sides.
The answer is −∞.
Where students go wrong
Calling the limit infinite whenever the bottom is zero. If the top is zero too, the form is 0/0: factor and cancel first, because it may be a hole with a finite limit.
Also called limits at essential discontinuities, limits to infinity, vertical asymptote limits or unbounded limits.
Questions about these worksheets
Yes. Every infinite limits sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the infinite limits questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Giving infinity for the two-sided limit when the two sides disagree. Across a simple pole one side runs up and the other runs down, so there is no single answer and the limit does not exist.