MA241-002 Summer I 2008 Test 2: Mathematics Review Sheet, Study notes of Calculus

Download MA241-002 Summer I 2008 Test 2: Mathematics Review Sheet and more Study notes Calculus in PDF only on Docsity! MA241-002, Summer I 2008 Test 2 review sheet Disclaimer: “This review sheet is only intended to give you some guidance, and thus should not be taken as an exhaustive listing of possible test question topics. Do not expect this every time.” Calculators which are not capable of symbolic manipulation are allowed on this test (i.e., no TI-89s, TI-92s, or equivalent). No other notes or aids will be allowed on this test. For those of you with a TI-89/92, you’ll need to either borrow another calculator or see me to make other arrangements. The test will cover §§6.2-5, 7.1-7.4 (see comment on §7.4 below). Note: Unless you are explicitly told not to, you will be expected to fully evaluate all definite integrals that arise in the course of working a problem. §6.2 You need to be able to set up (and evaluate) the integral for the volume of solids of revolution. You will have to decide which method to use based on the problem(s) given. Even if not explicitly asked to, you should sketch the region being rotated to get an idea of what method will work the best. If you need to find an intersection point for two functions, you may use your calculator to make an educated guess of where it is, but you need to plug your guess back into the functions to verify that it is correct. §6.3 You need to know the arc-length formulas for both parametric equations and curves of the form y = f(x). I will probably not ask you to complete the integration, but in the event that I do, the function(s) will be contrived such that the algebra works out relatively well. §6.4 You need to know the formula for the average value of a continuous function over an interval. You also need to be able to apply the Mean Value Theorem for Integrals to find c such that f(c) = fave. §6.5 You need to be able to set up (and evaluate) the integrals to find the work required to lift an object, work required to pump out a tank of water, and the hydrostatic force on a vertical submerged plate. You may also be asked to explain where each part of your integral is coming from. Even if not explicitly asked to, it is helpful to draw a picture of the situation, sketch in a coordinate system, and indicate where everything is with respect to that coordinate system. Moments and centers of mass will not on this test or on the final. As I said in class, the only time 1