University functions, limits and continuity quiz to download as PDF

This University functions, limits and continuity quiz has 10 short questions for pupils aged 18-19. Type your answer, check it straight away and read the explanation when you get one wrong.

University functions, limits and continuity quiz: the 10 questions

\(\lim_{x\to1}\frac{x^2-1}{x-1}\)?
\(\lim_{x\to0}\frac{\tan x}{x}\)?
\(\lim_{x\to\infty}\frac{1}{x^2}\)?
Name the theorem that guarantees a root when \(f(a)f(b)<0\) for continuous f.
True or false: \(\lim_{x\to a}f(x)\) depends on \(f(a)\).
What is \(\delta\) for \(\lim_{x\to a}(5x)\) given \(\varepsilon\)?
\(\lim_{x\to0}\frac{e^x-1}{x}\)?
Is \(1/x\) continuous on \((0,\infty)\)?
\(\lim_{x\to0^+}\frac{|x|}{x}\)?
Which limit law fails for \(\lim f/g\) if \(\lim g=0\)?

How to use this University functions, limits and continuity quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the functions, limits and continuity lesson and try again later. After that, try the multiple choice questions or the functions, limits and continuity worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.