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A6 - t increases from 0 to 2 π 4 In parts(a(b find the...

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Math 128: Assignment 6 due Wednesday, Nov 2 by 4:30 pm Koray Karabina ([email protected]) 1. Sketch the graph of the parametric curve C : x = t 3 + 3 t, y = t 2 , -∞ < t < . 2. Let C be the parametric curve defined by the parametric equation: x = t 3 - 4 t, y = t 2 , -∞ < t < (a) Sketch the graph of the parametric curve C . (b) Let R be the closed loop bounded by C . Find the area of the region R . 3. Find the length of the parametric curve C : x = t 2 sin t, y = t 2 cos t, 0 t 2 π . You may use (without proving) that C is travarsed exactly once as
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Unformatted text preview: t increases from 0 to 2 π . 4. In parts (a)-(b), find the exact area of the surface obtained by rotating the given curve about the x-axis. (a) C : x = t 3 , y = t 2 , ≤ t ≤ 1. (b) C : x = 3 t-t 3 , y = 3 t 2 , ≤ t ≤ 1. 5. In parts (a)-(c), transform the given polar equation to a Cartesian equation . (a) r = 2 1-2 sin θ (b) r = sec θ (1 + tan θ ) (c) r = 1 1-cos θ 6. This question has been moved to Assignment 7....
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