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242review-chapter10

242review-chapter10 - Math 242 Review Chapter 10 Highlights...

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Math 242 Review — Chapter 10 Highlights For slope or concavity of parametric curves, use the following: dy dx = dy dt dx dt d 2 y dx 2 = d dx dy dx = d dt ( dy dx ) dx dt The latter equation comes from d dx ( u ) = du dt dx dt . For converting between rectangular and polar coordinates, remember x = r cos θ y = r sin θ r 2 = x 2 + y 2 Be aware of how to correctly interpret polar coordinates when r is negative . If you define a polar curve with an equation r = f ( θ ), then you can regard it as a parametric curve x = f ( θ ) cos θ , y = f ( θ ) sin θ . For example, if r = e θ , then x = e θ cos θ and y = e θ sin θ . You can then say dx = e θ cos θ - e θ sin θ and dy = e θ sin θ + e θ cos θ , and so on. Area in polar coordinates is given by Z b a 1 2 r 2 . You find a and b by drawing a picture and/or considering where r = 0. ELLIPSE: Two special points, “focuses” F 1 and F 2 (distance to F 1 ) + (distance to F 2 ) = constant PARABOLA: One special point, “focus” F ; one special line, “directrix” L (distance to F ) = (distance to L ) HYPERBOLA:

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242review-chapter10 - Math 242 Review Chapter 10 Highlights...

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