ma100_hw3

ma100_hw3 - -10-5 5 x-axis-10-5 5 y-axis-10-5 5 10 z-axis...

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Homework answer 3 Sec 12.7 24. It is an elliptic paraboloid. 26. It is a hyperboloid of two sheets. 28. It is a hyperboloid of one sheet. Sec 12.8 18. z = r cos θ z = x It is a plane. 28. ρ sin 2 φ = 1 x 2 + y 2 = 1 It is a cylinder. Sec 13.1 22(a). ~ r ( t ) = (1 - t )( ~ i + ~ j ) + t ~ k ; 0 6 t 6 1 22(b). ~ r ( t ) = ~ i + ~ j + (1 - t ) ~ k ; 0 6 t 6 1 32. ~ r ( t ) = 9 cos t ~ i + 4 sin t ~ j + t ~ k Sec 13.2 28. ~ r ( t ) = 4 cos t ~ i - 3 t ~ j when t = π 3 , ~ r ( π 3 ) = (2 , - π ). ~ r 0 ( t ) = - 4 sin t ~ i - 3 ~ j The vector equation of tangent line is ~ r ( π 3 ) + λ~ r 0 ( π 3 ) = (2 , - π ) + λ (2 3 , 3) 38. Z < te t , ln t > dt = < te t , t ln t > - Z < e t , 1 > dt = < te t - e t , t ln t - t > + ~ c 58. d dt [ ~u · ( ~v × ~w )] = ( d~u dt ) · ( ~v × ~w ) + ~u · d ( ~v × ~w ) dt = ( d~u dt ) · ( ~v × ~w ) + ~u · ( d~v dt × ~w ) + ~u · ( ~v × d~w dt ) 1
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u**2+4*v**2, u, v 0 1 2 3 4 x-axis -3 -2 -1 0 1 2 y-axis -3 -2 -1 0 1 2 3 z-axis sqrt(9+3*u**2+3*v**2), u, v -sqrt(9+3*u**2+3*v**2), u, v -10 -5 0 5 x-axis -4 -2 0 2 4 y-axis -4 -2 0 2 4 z-axis 2*cos(u)/cos(v), 4*tan(v), 2*sin(u)/cos(v)
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Unformatted text preview: -10-5 5 x-axis-10-5 5 y-axis-10-5 5 10 z-axis x--1.5-1-0.5 0.5 1 1.5 x-axis-2-1.5-1-0.5 0.5 1 1.5 y-axis-3-2-1 1 2 3 z-axis cos(u), sin(u), v--1.5-1-0.5 0.5 1 1.5 x-axis-2-1.5-1-0.5 0.5 1 1.5 y-axis-3-2-1 1 2 3 z-axis 0.5 1 1.5 2 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x-axis y-axis z-axis (0,0,1) (1,1,0) 0.5 1 1.5 2 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 y-axis x-axis (1.1.1) (1.1.0)-10-5 5 10-10-5 5 10 2 4 6 8 10 x-axis y-axis...
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ma100_hw3 - -10-5 5 x-axis-10-5 5 y-axis-10-5 5 10 z-axis...

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