7. Cauchy Integral Formula

Liouville’s Theorem — Quiz

Test your understanding of liouville’s theorem with 5 practice questions.

Practice Questions

Question 1

Which statement is Liouville's theorem?

Question 2

Suppose $f$ is entire and $|f(z)| \le 3$ for all $z \in \mathbb{C}$. What must be true?

Question 3

Which function is entire but not bounded on $\mathbb{C}$, so Liouville's theorem cannot be applied to conclude it is constant?

Question 4

If an entire function has a finite limit as $|z| \to \infty$, what can be concluded?

Question 5

How is Liouville's theorem used in the usual proof of the fundamental theorem of algebra?