12.6-13.2

# 12.6-13.2 - r t = ± 10-t 2 t 5 t 3 ² and the position of...

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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 and s ( t ) = t - 4 , 1 2 t, - t 2 - 4 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.
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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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