IDZ Ryabushko 4.2 Variant 19
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№1 Build surfaces and determine their type a) z = 4 - x2 - y2; b) 3x2 + 12y2 + 4z2 = 48.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) x2 - 9y2 = 9; Ox; b) 3y2 = z; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = 2x; y = 0; x = 2; z = 2x2 + y2; z = 0.
b) x2 + y2 + z2 = 16; x2 + y2 ≤ 4; x ≥ 0.
№2 Write down the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture: a) x2 - 9y2 = 9; Ox; b) 3y2 = z; Oz.
№3 Build a body bounded by the indicated surfaces: a) y = 2x; y = 0; x = 2; z = 2x2 + y2; z = 0.
b) x2 + y2 + z2 = 16; x2 + y2 ≤ 4; x ≥ 0.
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