# Exam III - Math 3B Honors Castroconde Exam III(11.1 11.2...

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Math 3B Honors – Castroconde Name: Exam III (11.1, 11.2, Chapter 12) I.D.#: Page 1 2 3 4 5 6 Total Points To get full credit, you must show all your work. 1. Consider the curve described by parametric equations t y t x 2 2 cos , sin = = . a. Eliminate the parameter to get a Cartesian equation of the curve. b. Sketch the curve and explain how the curve is traced as the parameter increases. 2. Find an equation for the tangent to the parametric curve t t y t x + = + = 3 4 , 1 at the point corresponding to t = -1. 3. For which values of t is the parametric curve defined in problem 2 concave up?

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4. Give a parametric description for the circle centered at the origin and radius 2. Use your parametric equations to find the circumference of the circle as the arc length of the curve. 5. Find the area of the surface obtained by rotating the parametric curve , 1 0 , 3 , 3 2 3 = - = t t y t t x about the x -axis. For all questions dealing with convergence of series, every test used must be named.
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Exam III - Math 3B Honors Castroconde Exam III(11.1 11.2...

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