cal 3 Determine the type of quadric surface and sketch the graph: (x/2)2 - y2 +

Question

cal 3

Determine the type of quadric surface and sketch the graph: (x/2)2 - y2 + (z/2)2 = 1. Find the intersection of the planes x + y + z = 1 and 3x - 2y + z = 5. Determine the domain of the vector-valued function .Calculate the derivative at t = 3. assuming that r1rightarrow(3) = 1,1,0 , r2rightarrow(3) = 1,1,0 , r'1rightarrow(3) = 0,0,1 , r'2rightarrow(3) = 0,2,4 . d/dt(etr2rightarrow(t)) d/dt(r1rightarrow times r2rightarrow) A particle located at (1,1,0) at time t = 0 follows a path whose velocity vector is (t) = 1, t, t2 . Find the particle's location at t = 2.

Explanation / Answer

5. Calculate distance along each direction. Note: t varies from 0 to 2 For x-axis: Final position= 1 + 1*2= 3 For y-axis: Final position= 1 + t.dt= 1+ (t^2)/2 = 3 For z-axis: Final position= 0 + (t^3)/3= 8/3 Position= (3,3,8/3)

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