This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Version 066 Exam03 Gilbert (56380) 1 This printout should have 12 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points For which of the following quadratic rela tions is its graph a twosheeted hyperboloid? 1. z = y 2 x 2 2. x 2 + y 2 z 2 = 1 3. z 2 = x 2 + y 2 4. z 2 x 2 y 2 = 1 correct 5. 2 x 2 + y 2 + 3 z 2 = 1 6. z = x 2 + y 2 Explanation: The graphs of each of the given quadratic relations is a quadric surface in standard posi tion. We have to decide which quadric surface goes with which equation  a good way of do ing that is by taking plane slices parallel to the coordinate planes, i.e. , by setting respec tively x = a , y = a and z = a in the equations once weve decided what the graphs of those plane slices should be. Now as slicing of shows, slices of this twosheeted hyperboloid by z = a are circles for  a  sufficiently large, while the slices by x = 0 and y = 0 are hyperbolas opening up and down. Only the graph of z 2 x 2 y 2 = 1 has these properties. keywords: Surfaces, SurfacesExam, 002 10.0 points The radius of a right circular cylinder is decreasing at a rate of 2 inches per minute while the height is increasing at a rate of 4 inches per minute. Determine the rate of change of the volume when r = 3 and h = 8. 1. rate = 52 cu.in./min. 2. rate = 60 cu.in./min. correct 3. rate = 44 cu.in./min. 4. rate = 48 cu.in./min. 5. rate = 56 cu.in./min. Explanation: The volume cylinder of a cylinder of height h and radius r is given by V ( r, h ) = r 2 h . Thus the rate of change of V with respect to t is V t = (2 rh r t + r 2 h t ) But r t = 2 , h t = 4 . Consequently, V t vextendsingle vextendsingle vextendsingle ( r =3 , h =8) = 60 cu.in./min. . 003 10.0 points Determine f y when Version 066 Exam03 Gilbert (56380) 2 f ( x , y ) = 2 x y x + 2 y ....
View Full
Document
 Spring '07
 Sadler
 Multivariable Calculus

Click to edit the document details