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Unformatted text preview: Practice Exam Parametrics: No Paramedics. (hopefully) David Imberti April 23, 2010 1 Introduction I have to apologize first of all. This guide is probably going to be more significantly rushed than the previous guides. Mainly because I’m getting rushed for time in my life at the moment, but also because there really isn’t a whole lot in this last section. 2 Warm-up: Since It’s the Last One. Maybe It Should Be Called a Cool-Down? (1) Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = e √ t ,y = t- lnt 2 ,t = 1 (2) Find the area enclosed under an ellipse. (3) Find the length of the curve x = 1 + 3 t 2 ,y = 4 + 2 t 3 , ≤ t ≤ 1. (4) Find the polar coordinates of (1 ,- 2) with 0 ≤ θ < 2 π (5) Find the tangent line to rsinθ = 1 at θ = π 4 . 3 Parametric: Something Like a Parachute and a Distance Q: What even is this stuff? A: Is just a new way to play with y = f ( x ). Only you’re splitting it up into y = g ( t ) ,x = f ( t ). It still makes curves, so you can still do Calculus. Q: FEED ME FORMULAS. A: BLEH: Finding slope: dy dx = dx dt dy dt Finding area: A = R b a g ( t ) f ( t ) dt Finding arc length: L = R b a q ( dx dt ) 2 + ( dy dt ) 2 dt Q: HOW DO I USE THESE?...
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- Spring '09
- Parametric Equations, Polar coordinate system, Conic section