12.6-13.2

12.6-13.2 - r ( t ) = ± 10-t, 2 t, 5 t 3 ² and the...

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MATH 231 Group Work Quiz Related 1. Classify and sketch the following surfaces: (a) z = 2 x 2 + y 2 (b) z 2 = x 2 + 1 3 y 2 (c) 1 + 5 z 2 = 7 x 2 - y 2 (d) 4 + z 2 = x 2 + y 2 2. What is the domain of the vector function r ( t ) = D 2 - t, ln t, t 2 - 1 t - 1 E ? 3. At what point(s) do the curves r ( t ) = ± t 2 ,t 2 + 1 , 4 t ² and s ( t ) = ± t - 4 , 1 2 t, - t 2 - 4 ² intersect? 4. Find a vector function that represents the curve of intersection of z 2 = x 2 + y 2 and 2 x + 3 y - z = 1. 5. There are headhunters in the woods of Shenandoah. One day, a man sets out on a backpacking trip through the wilderness and is spotted by the chief of the headhunters. With exquisite aim, the headhunter throws his spear at the man. If the man’s position is modelled by the space curve
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Unformatted text preview: r ( t ) = ± 10-t, 2 t, 5 t 3 ² and the position of the spear is modelled by the space curve s ( t ) = h 2 t,t, 9 t + 4 i . Does the chief get a new plaque for his wall? Do the man and the spear cross paths? 6. Evaluate the integral: (a) Z ³ e t i + 1 t j + t 3 k ´ dt (b) Z π (sin t i + cos t j + k ) dt 7. If u ( t ) = r ( t ) · [ r ( t ) × r 00 ( t )], show that u ( t ) = r ( t ) · [ r ( t ) × r 000 ( t )]. 1...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.

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