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13 Nov 2019
For the questions that follow, you will need the following objects. ·The surface S, given by the part of +z2-9z? which is above the xy-plane. . The curve C, given by t) =å3t cos(t), t sin(t)) for 0 t 21. . The two-dimensional vector field F, whose vectors are the gradient vectors of S = f(x,y). 1. Sketch some of the level curves of S on the ay-plane, and use these level curves to sketch the vector field F 2. Verify that the curve C lies on the surface S. What is the equation of the curve Cı which is the projection of C on the cy plane? 3. Is Jo, F di zero or nonzero? Explain, using your picture. 4. Calculate F.d 5. Find two non-parallel vectors which are tangent to S at the point ( 0,5). Could your method of finding these vectors be used on other surfaces at other points?
For the questions that follow, you will need the following objects. ·The surface S, given by the part of +z2-9z? which is above the xy-plane. . The curve C, given by t) =å3t cos(t), t sin(t)) for 0 t 21. . The two-dimensional vector field F, whose vectors are the gradient vectors of S = f(x,y). 1. Sketch some of the level curves of S on the ay-plane, and use these level curves to sketch the vector field F 2. Verify that the curve C lies on the surface S. What is the equation of the curve Cı which is the projection of C on the cy plane? 3. Is Jo, F di zero or nonzero? Explain, using your picture. 4. Calculate F.d 5. Find two non-parallel vectors which are tangent to S at the point ( 0,5). Could your method of finding these vectors be used on other surfaces at other points?
Casey DurganLv2
23 Jan 2019