14. Final Review

Key Themes In Final Review — Quiz

Test your understanding of key themes in final review with 5 practice questions.

Practice Questions

Question 1

Which property of the real numbers says that every nonempty set bounded above has a least upper bound in the real numbers?

Question 2

Which theorem says that a continuous function on a closed interval $[a,b]$ attains both a maximum and a minimum there?

Question 3

What does the Bolzano-Weierstrass theorem say about a bounded sequence in $\mathbb{R}$?

Question 4

What is true about every Cauchy sequence in $\mathbb{R}$?

Question 5

Suppose $f$ is continuous on $[a,b]$ and $f(a)$ and $f(b)$ have opposite signs. What conclusion follows?