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: Practice Exam 1 David Imberti April 23, 2010 1 A Retroactice Guide: Looking into the Past into the Future 1.1 Introduction So, I originally made these practice exam/guide things as an experiment to see if they were at all helpful, and only thought to try making these after the first exam. Ive gotten a lot of feedback that they were helpful and have since been trying to make them of the same quality for you guys. Seeing as how the final is comprehensive, and I still see some issues with shell v. cylinder integration, I decided to make a retroactive practice exam in the hopes itll help you for the final. I might make another one for the small bit about parametric equations to have a complete set for this course :U. 2 Warmup: Exercises for the SOUL (1) Determine if < 1 , 3 , 4 > and < 1 , 1 , 1 > are perpendicular or parallel. (2) Find a vector perpendicular to the space spanned by < 1 , 1 , 1 > and < 1 , 1 , 2 > . (i.e., find a vector perpendicular to both.) (3) Find a unit vector of < 3 , 4 , > going in the opposite direction. (4) Find proj < 6 , 3 , 9 > < 4 , 2 , 6 > . (5) Find the area in [0 , 1] between 1 x 2 and the xaxis. (6) Find the area in [ 3 , 0] between x 2 + 3 x and the x = 2. (7) y = 1 x on [1 , 2] about the xaxis. (8) y = 1 x on [1 , 2] about the yaxis. (9) y = x 2 + 6 x 8 ,y = 0 about yaxis. (10) y = x 2 + 6 x 8 ,y = 0 about xaxis. (11) y = 5 ,y = x + 4 x about x = 1. (12) x = ( y 3) 2 ,x = 4 about y = 1. (13) x 2 + ( y 1) 2 = 1 about the yaxis. (14) 10J are needed to stretch a spring from 10 cm to 20 cm and another 20J is need to stretch from 20 to 30cm. What is the natural length of the spring? (15) A chain is lying on the ground and is 10m long and its mass is 80kg. How much work is required to raise one end of the chain to a height of 6m? 3 THIS WAS SO LONG AGO Q: THIS WAS FROM THE BEGINNING OF THE SEMESTER. I DONT REMEMBER HOW TO DO ANY OF THIS. HOW DO I INTEGRATE AGAIN? 1 A: Dont worry about it, there are only a very few number of subjects on the first exam to cover. (also, see practice exam 2 for a lot of integration tips, but seriously, antiderivatives) Q: O.K., YOU KNOW THE DEAL, WHAT DO I GOTS TO KNOW? A: Got to know...Either way, there are really 4 main subjects: (1) Vector stuff. (2) Finding areas by integration. (3) Finding volumes by the shell/disk method. (4) Finding volumes by the cylinder method. (5) Finding work. Q: ALRIGHT, I GOT A HALF TANK OF GAS, TWO HOURS TO CHICAGO, ITS DARK, AND IM WEARING SUNGLASSES. LETS DO THIS. 3.1 Vectors: Pointing the Way to a NEW YOU Q: VECTORS? WAIT, ARENT I TAKING A COURSE ABOUT INTEGRATION? A: Yes, you are. Just deal with it for now, youll see why this came up if you take Calc III....
View
Full
Document
 Spring '09
 Shell Method

Click to edit the document details