Engineering Calculus Notes 423

Engineering Calculus Notes 423 - 12 = 0 2. For each...

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3.10. QUADRATIC CURVES AND SURFACES 411 The resulting surface consists of two bowl-like parts, and is called a hyperboloid of two sheets (Figure 3.50 ). x y z Figure 3.50: Hyperboloid of Two Sheets x 2 + y 2 = z 2 1 Exercises for § 3.10 Practice problems: 1. Identify each curve below; sketch if possible: (a) 5 x 2 6 xy + 5 y 2 = 8 (b) 17 x 2 12 xy + 8 y 2 = 20 (c) 3 x 2 + 8 xy 3 y 2 = 1 (d) 3 x 2 8 xy 3 y 2 + 1 (e) 4 xy = 16 (f) xy + y 2 = 1 (g) x 2 x + y 2 + y + 2 xy = 0 (h) 5 x 2 + 5 y 2 + 6 xy + 8 x + 8 y
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Unformatted text preview: 12 = 0 2. For each equation below, take a few well-chosen slices and try to sketch the surface it denes: (a) x 2 y + 2 z = 4 (b) x 2 y + 4 z 2 = 4 (c) x 2 y z 2 = 0 (d) x 2 + 4 y 2 + 9 z 2 = 36 (e) x 2 4 y 2 + 9 z 2 = 36 (f) x 2 4 y 2 9 z 2 = 36 (g) x 2 4 y 2 9 z 2 = 0 (h) x 2 4 y 2 9 z 2 = 36...
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