3. Functions of Several Variables

Limits And Continuity In Higher Dimensions — Quiz

Test your understanding of limits and continuity in higher dimensions with 5 practice questions.

Practice Questions

Question 1

What is the value of $\lim_{(x,y)\to(2,-1)} (x^2+xy+y^2)$?

Question 2

Which statement best describes what it means for a function $f$ to be continuous at a point $(a,b)$?

Question 3

What is the value of $\lim_{(x,y)\to(1,1)} \frac{x^2-y^2}{x-y}$?

Question 4

Does $\lim_{(x,y)\to(0,0)} \frac{x^2-y^2}{x^2+y^2}$ exist?

Question 5

What is the value of $\lim_{(x,y)\to(0,0)} \frac{x^2y}{x^2+y^2}$?