Maple Problem Set #4

Before doing these problems, create clean new worksheet and put your name at the top. These problems require you to use the plots library. You can load in this library with the command:

[> with(plots);

1.

Render the surface

$${\v r} (s,t) = \langle 3 \cos(s) \sin(t), 2 \sin(s) \sin(t), 5\cos(t)\rangle.$$

Prove that this surface is an ellipsoid centered at the origin with axes 3, 2 and 5, respectively.

2.

Parametrize a sphere of radius 3 centered at (1,0,2), and render it in Maple.

3.

Parametrize the surface

x+y+z=1

restricted to the first octant. Be careful to find the appropriate domain for your parameters.

4.

Use Maple to find dA for

$${\v r} (s,t) = \langle s,t,\sin (s) \sin (t)\rangle.$$