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) = x^{3}  3xy^{2} Click here for a hint. Click here to check your answer to problem 1. 2. f(x,y) = 2xy(x^{2}  y)(x^{2} + y) Click here for a hint. Click here to check your answer to problem 2. 3. f(x,y) = (1  x^{2}  y^{2})x Click here for a hint. Click here to check your answer to problem 3. 4. f(x,y) = (1  x^{2}  y^{2})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} + y^{2} = 1 around the zaxis. Click here for a hint. Click here to check your answer to problem 5. 6. f(r,t) = r^{2}cos(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.
