Show all of your work. Make all graphs large and draw them as clearly and neatly...

 

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Show all of your work. Make all graphs large and draw them as clearly and neatly as possible. 1. (a) Graph the ellipse given by 9 25 in the zz-plane and label its vertices. (b) Now consider the equation from part (a) as a generating curve for a cylinder in space. Sketch the cylinder. Make this graph large (about half a page) since you will have to include answers to parts (c) and (d) on the same graph. (c) Let r(t) = 3 cos ti + tj +5 sin tk with -2 ≤t≤ 2. Draw the space curve given by r(t) on your sketch from part (b). (d) Find r'(t) and draw r'(-27), r'(0), and r'(7/2) on you sketch from part (b). (e) Find another space curve q(t) that lies on the cylinder from part (b). Be sure to justify that q(t) lies on the cylinder. You do not need to sketch q(t), just define it. Show all of your work. Make all graphs large and draw them as clearly and neatly as possible. 1. (a) Graph the ellipse given by 9 25 in the zz-plane and label its vertices. (b) Now consider the equation from part (a) as a generating curve for a cylinder in space. Sketch the cylinder. Make this graph large (about half a page) since you will have to include answers to parts (c) and (d) on the same graph. (c) Let r(t) = 3 cos ti + tj +5 sin tk with -2 ≤t≤ 2. Draw the space curve given by r(t) on your sketch from part (b). (d) Find r'(t) and draw r'(-27), r'(0), and r'(7/2) on you sketch from part (b). (e) Find another space curve q(t) that lies on the cylinder from part (b). Be sure to justify that q(t) lies on the cylinder. You do not need to sketch q(t), just define it.

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1 a To graph the ellipse given by 19x2 125y2 1 in the xyplane and label its vertices First lets rewr... View the full answer