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6th - z = xy 6 If r t =< t,t 2,t 3> ﬁnd r t T(1 r 00...

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MATH 120 WEEK 6 (RECITATION QUESTIONS) 1. Reduce the equation 4 y 2 + z 2 - x - 16 y - 4 z + 20 = 0 to one of the standard forms, classify the surface, and sketch it. 2. Sketch the region bounded by the surfaces z = p x 2 + y 2 and x 2 + y 2 = 1 for 1 z 2. 3. Find an equation for the surface obtained by rotating the parabola y = x 2 about the y -axis. 4. Show that the curve with parametric equations x = t cos t , y = t sin t , z = t lies on the cone z 2 = x 2 + y 2 , and use this fact to help sketch the curve. 5. Find a vector function that represents the curve of intersection of the two surfaces.The cylinder x 2 + y 2 = 4 and the surface
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Unformatted text preview: z = xy . 6. If r ( t ) = < t,t 2 ,t 3 > , ﬁnd r ( t ) , T (1), r 00 ( t ), and r ( t ) × r 00 ( t ). 7. At what point do the curves r 1 ( t ) = < t, 1-t, 3 + t 2 > and r 2 ( s ) = < 3-s,s-2 ,s 2 > inter-sect? Find their angle of intersection correct to the nearest degree. 8. If r ( t ) 6 = 0, show that d dt | r ( t ) | = 1 | r ( t ) | r ( t ) · r ( t ). [Hint: | r ( t ) | 2 = r ( t ) · r ( t ) ] 9. Find the length of the curve r ( t ) = t 2 i + 2 t j + ln t k , 1 ≤ t ≤ e . 1...
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