Limits of Functions: Level 1 Challenges Practice Problems Online

$\boxed{\begin{array}{c|r:r:r:r:r} x & 0.1 & 0.01& 0.001& 0.0001& 0.00001\\ \hline \lfloor x \rfloor & 0 & 0 & 0 & 0 & 0 \end{array}}$

By looking at the table above, is it true that as $x$ approaches 0, then $\lfloor x \rfloor$ approaches 0 as well?
That is, is $\displaystyle \lim_{x\to0} \lfloor x\rfloor = 0$ correct?

Notation: $\lfloor \cdot \rfloor$ denotes the floor function.

$\Large \lim_{x\to0} \dfrac{x}{x!} = \, ?$

Note: Treat $x! = \Gamma(x+1)$ .

$\lim_{x\to\infty} \dfrac{\sin x}x = \, ?$

Find $\displaystyle\lim_{x\rightarrow 3}$ $\dfrac{x^2-9}{x-3}$

$\large \lim_{x \to 1} \dfrac{|x-1|}{x-1} = \, ?$

Intro

Concept Quizzes

Challenge Quizzes

Limits of Functions: Level 1 Challenges

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.