Sign up to access problem solutions.

Already have an account? Log in here.

What happens when a function's output isn't calculable directly – e.g., at infinity – but we still need to understand its behavior? That's where limits come in. See more

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

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.

Sign up to access problem solutions.

Already have an account? Log in here.

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

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

Sign up to access problem solutions.

Already have an account? Log in here.

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

Sign up to access problem solutions.

Already have an account? Log in here.

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

Sign up to access problem solutions.

Already have an account? Log in here.

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

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...