Fall 2010 Math 251 Exam 4: Solutions c 2010 Art Belmonte Tue, 07/Dec
1. Use a line integral to find the area of the lateral surface over the circle C : x2 + y2 = 4 in the xy-plane and under the surface z = x2 - y2 + 4. Let z = f (x, y) = x2 - y2 + 4.
Fall 2010 Math 251 Exam 3A: Solutions c 2010 Art Belmonte Tue, 09/Nov
Refer to diagrams drawn on your exam. 1. Find the volume of the solid in the first octant bounded by the circular cylinders x2 + z2 = 9 and y2 + z2 = 9, and the coordinate planes. Recta
Fall 2010 Math 251 Exam 2A: Solutions c 2010 Art Belmonte Tue, 19/Oct
1. Describe level curves of f (x, y) = 25 - x2 - y2 . Sketch the level curves for the c-values c = 0, 3, 4 on the grid below.
Problem 1 5
3. Using the Chain Rule, compute w/t when s = 3
Fall 2010 Math 251 Exam 1A: Solutions c 2010 Art Belmonte Tue, 28/Sep
1. Find the center C and radius r of the sphere 9x2 + 9y2 + 9z2 - 18x + 6y - 72z + 73 = 0. We'll complete the squares then read off the center and radius. First divide the equation by 9
Introduction to Lego Building
Lesson Objective: To familiarized the students with Lego vocabulary and specific building pieces. Learning Objective: To learn the names and purposes of Lego building pieces Materials: Lego Simple Machine kits or other Lego b