3D Practice

3D Practice Problems

Here are some functions that you can use to practice the techniques you've learned so far. Try graphing them yourself first, then check your answer.

1. f(x,y) = x³ - 3xy²

Click here for a hint.

Click here to check your answer to problem 1.

2. f(x,y) = 2xy(x² - y)(x² + y)

Click here for a hint.

Click here to check your answer to problem 2.

3. f(x,y) = (1 - x² - y²)x

Click here for a hint.

Click here to check your answer to problem 3.

4. f(x,y) = (1 - x² - y²)xy

Click here for a hint.

Click here to check your answer to problem 4.

5. Revolving a 2D graph around one of the three axes yields a surface of revolution. Graph the surface of revolution formed by revolving the circle (x - 3)² + y² = 1 around the z-axis.

Click here for a hint.

Click here to check your answer to problem 5.

6. f(r,t) = r²cos(4t)

Click here for a hint.

Click here to check your answer to problem 6.

7. f(r,t) = sin(cr), c = 2pi

Click here for a hint.

Click here to check your answer to problem 7.




	3D Practice Problems Here are some functions that you can use to practice the techniques you've learned so far. Try graphing them yourself first, then check your answer. 1. f(x,y) = x³ - 3xy² Click here for a hint. Click here to check your answer to problem 1. 2. f(x,y) = 2xy(x² - y)(x² + y) Click here for a hint. Click here to check your answer to problem 2. 3. f(x,y) = (1 - x² - y²)x Click here for a hint. Click here to check your answer to problem 3. 4. f(x,y) = (1 - x² - y²)xy Click here for a hint. Click here to check your answer to problem 4. 5. Revolving a 2D graph around one of the three axes yields a surface of revolution. Graph the surface of revolution formed by revolving the circle (x - 3)² + y² = 1 around the z-axis. Click here for a hint. Click here to check your answer to problem 5. 6. f(r,t) = r²cos(4t) Click here for a hint. Click here to check your answer to problem 6. 7. f(r,t) = sin(cr), c = 2pi Click here for a hint. Click here to check your answer to problem 7.