X2 2 31 x y z 4 spherical 64 4 sin 4 sin 4 cos 6 4

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Unformatted text preview: r 10, , , spherical 62 10 sin 2 10 6 arccos 3 13 , arccos 3 , 13 5 arccos 13 13, , arccos 5 , spherical 13 6 z 10 cos 2 0 2 13, spherical 6 10, , 0 , cylindrical 6 61. r 36, , 2 , spherical 36 sin 36 63. r 6, , , spherical 63 6 sin 3 33 65. r 8, 7 , , spherical 66 8 sin 7 6 6 4 sin 2 6 z cos 36 cos 2 0 z 6 cos 3 3, 3 6 3 z 4, 8 cos 6 83 2 36, , 0 , cylindrical , 3 , cylindrical 7 , 4 3 , cylindrical 6 Rectangular 67. 4, 6, 3 69. 4.698, 1.710, 8 71. 73. 3, 75. 77. 7.071, 12.247, 14.142 2, 2 Cylindrical 7.211, 0.983, 3 5, , 8 9 14.142, 2.094, 14.142 3.606, 0.588, 2 1.5 Spherical 7.810, 0.983, 1.177 9.434, 0.349, 0.559 20, 2 , 34 0.588, 1.064 4.123, 54 3 ,, 23 2 3.536, 3.536, 2.095, 6 5 2.833, 0.490, 5, 3 , 4 5 3.206, 0.490, 2.058 7.071, 2.356, 2.356 6.946, 5.642, 0.528 79. 2.804, 3.5, 2.5, 6 [Note: Use the cylindrical coordinates 3.5, 5.642, 6 85. r 2 z, x 2 y2 81. r 5 83. 5 Sphere Matches graph (c) z Cylinder Matches graph (d) 87. Rectangular to cylindrical: r 2 tan z Cylindrical to rectangular: x y z z r cos r sin z x2 y x y2 Paraboloid Matches graph (f) 89. Rectangular to spherical: 2 x2 y x y2 z2 tan arccos Spherical to rectangular: x y z sin sin cos x2 cos sin z y2 z2 256 91. x2 Chapter 10 y2 z2 z2 16, 16 16 4 Vectors and the Geometry of Space 93. x2 y2 z2 z2 2z 2z 0 0, r 2 0, z 1 2 (a) r 2 (b) 2 (a) r 2 (b) 2 1 0, 2 cos 2 cos 2 cos 95. x2 y2 4y 4r sin , r 4 sin sin , 4 sin 4 sin csc 0, 97. x2 y2 9 r 2 sin2 9 cos2 sin2 2 (a) r 2 (b) 2 (a) r 2 cos2 r2 (b) 2 9, sin 2 4 sin sin sin 4 sin , sin sin2 sin2 cos2 cos2 sin2 sin2 , sin2 9, 2 9 2 9 csc2 cos2 sin2 103. 0 ≤ 0≤ 0≤ ≤2 ≤ 6 99. 0 ≤ ≤ 2 101. 0 ≤ ≤2 0≤r≤2 0≤z≤4 z 0≤r≤a r≤z≤a z a ≤ a sec z 5 a 3 2 1 x 2 3 x 2 3 y y a a y −a −a 30° x 105. Rectangular 0 ≤ x ≤ 10 0 ≤ y ≤ 10 0 ≤ z ≤ 10 10 z 107. Spherical 4≤ ≤6 −8 10 8 z 8 y x −8 y 10 x 109. z z sin , r y r y 1 1 y y and the cylinder r 1. The curve of intersection is the ellipse formed by the intersection of...
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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