Homework 17 Solution - Parametric Equations Tangent Lines Arc Length SUGGESTED REFERENCE MATERIAL As you work through the problems listed below you

# Homework 17 Solution - Parametric Equations Tangent Lines...

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Parametric Equations, Tangent Lines, & Arc Length SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should reference Chapter 10.1 of the rec- ommended textbook (or the equivalent chapter in your alternative textbook/online resource) and your lecture notes. EXPECTED SKILLS: Be able to sketch a parametric curve by eliminating the parameter, and indicate the orientation of the curve. Given a curve and an orientation, know how to find parametric equations that generate the curve. Without eliminating the parameter, be able to find dy dx and d 2 y dx 2 at a given point on a parametric curve. Be able to find the arc length of a smooth curve in the plane described parametrically. PRACTICE PROBLEMS: For problems 1-5, sketch the curve by eliminating the parameter. Indicate the direction of increasing t . 1. x = 2 t + 3 y = 3 t - 4 0 t 3 y = 3 2 x - 17 2 from (3 , - 4) to (9 , 5) 1
2. x = 2 cos t y = 3 sin t π t 2 π x 2 4 + y 2 9