MAT 265 Iowa State

Solutions to Even Problems Section 13.1: 2.) b.) Simple; not closed. c.) y = 3/2x. 4.) b.) Simple; not closed. c.) y = 1/2(x + 2). 6.) b.) Simple; not closed. c.) y = 2x - 6. 8.) b.) Simple; not closed. c.) y = 1/x. 10.) b.) Simple; not closed. c.)

Allen Math 265 A1 Practice Exam #2 Name: 1. Let f (x, y) = -8x2 + 48x - 2y 2 - 8y + 20. (a) Identify and write the equation for each of the level curves of this function for z = k, where k = 92, 68, 28, -28. (b) Consider the point p = 1, 2( 5 -

Allen Math 265 B1 Practice Exam #3 Name: 1. Find the volume of the tetrahedron trapped in the first octant beneath the plane 6x + 4y + 3z = 12. 2. Set up and evaluate the following integrals: (a) R 4 dA where R is the region trapped between y =

Allen Math 265 B2 Exam #2 Form B Name: 1. Let f (x, y) = 9y 2 - 72y - x2 - 4x + 131. (a) Identify the quadratic surface this equation describes. Set z = 9y 2 - 72y - x2 - 4x + 131. Completing the square yields z = 9(y 2 - 8x) - (x2 + 4x) + 131 z

Allen Math 265 B2 1. Let f (x, y) = 4x2 + 8x - y 2 + 6y - 33. Exam #2 Form A Name: (a) Identify the quadratic surface this equation describes. Set z = 4x2 + 8x - y 2 + 6y - 33. Completing the square yields z = 4(x2 + 2x) - (y 2 - 6y) - 33 z = 4(

Allen Math 265 B2 Homework #12 (20 points) Date Due: Thursday, April 19, 2007 Instructions: Please work the following problems on other pieces of paper. You must show all work and calculations in order to receive full credit. I would prefer to co

Allen Math 265 B2 Exam #1 Name: 1. A particle P has a trajectory path described by the vector equation r(t) = (t2 + 3)i - (6t + 7)j (a) Find the unit tangent vector, T (t). v(t) = 2ti - 6j. So v(t) = (2t)2 + (-6)2 = 4t2 + 36 = 2 t2 + 9. Therefo

Allen Math 265 B2 Exam #1 Name: 1. Find the center and radius of the sphere x2 + y 2 + z 2 + 6x - 4y - 14z + 13 = 0. Grouping x, y, and z terms together we get (x2 + 6x) + (y 2 - 4y) + (z 2 - 14z) = -13. Then complete the square as follows: (x2 +