University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

258

Pages:

1
Author:

Vivian Bernard

Workshop #1 1. For the problem below, we have the following rectangle and rectangular parallelepiped (3D box, hyperrectangle, rectangular prism). Determine the following using the rectangle. (a) Find the coordinates of each of the corners. (b) Find the midpoint of the diagonal which connects points P and R. (c) Find the length of the diagonal which connects points P and R. Determine the following using the 3D box. (d) Find the coordinates of each of the remaining six corners. (e) Find the midpoint of the diagonal which connects points F and C. (f) Find the length of the diagonal which connects points F and C. 2. Graph each of the following equations/inequalities twice. Your first graph of each should be in R2 (2D space, the xy-plane), and your second graph of each should be in R3 (3D space, xyz-space). (a) x = 1 (b) y > 5 (c) y = x (d) x2 + y 2 = 4 3. Write equations or inequalities that describe the set of points. Sketch a picture. (a) The plane perpendicular to the y-axis at (0, −4, 0). (b) The plane through the point (2, 5, −7) perpendicular to the x-axis. (c) The plane through the point (2, 5, −7) parallel to the xy-plane. (d) The circle of radius 2 centered at (−3, 1, 6) and lying in a plane parallel to the yz-plane.