3. Partial Derivatives

Limits And Continuity — Quiz

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

Practice Questions

Question 1

Evaluate the limit: $\lim_{(x,y) \to (0,0)} \frac{x^2 - y^2}{x^2 + y^2}$.

Question 2

Which of the following statements about the continuity of the function $f(x,y) = \frac{xy}{x^2 + y^2}$ at the point $(0,0)$ is true?

Question 3

Evaluate the limit: $\lim_{(x,y) \to (0,0)} \frac{x^3 y}{x^2 + y^4}$.

Question 4

Consider the function $f(x,y) = \sqrt{x^2 + y^2}$. Which of the following statements is true regarding its continuity?

Question 5

Find the limit: $\lim_{(x,y) \to (0,0)} \frac{x^2 y}{x^4 + y^2}$.