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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Exam 1 David Imberti April 23, 2010 1 A Retroactice Guide: Looking into the Past into the Future 1.1 Introduction So, I originally made these practice exam/guide things as an experiment to see if they were at all helpful, and only thought to try making these after the first exam. I’ve 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 it’ll 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 DON’T REMEMBER HOW TO DO ANY OF THIS. HOW DO I INTEGRATE AGAIN? 1 A: Don’t 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, IT’S DARK, AND I’M WEARING SUNGLASSES. LET’S DO THIS. 3.1 Vectors: Pointing the Way to a NEW YOU Q: VECTORS? WAIT, AREN’T I TAKING A COURSE ABOUT INTEGRATION? A: Yes, you are. Just deal with it for now, you’ll see why this came up if you take Calc III....
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 Spring '09
 Shell Method, Vector Space, Cartesian Coordinate System, Dot Product, Vector Motors, cylinder method

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