Engineering Calculus Notes 424

Engineering Calculus Notes 424 - (a) 3 x 2 8 xy + 3 y 2 + z...

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412 CHAPTER 3. REAL-VALUED FUNCTIONS: DIFFERENTIATION 3. For each equation below, complete the square, then take a few slices and sketch the locus: (a) x 2 + y 2 + z 2 2 x + 4 y + 2 z = 1 (b) x 2 + y 2 + z 2 2 x + 4 y + 2 z = 10 (c) 4 x 2 y 2 + 9 z 2 + 8 x + 2 y + 18 z = 12 (d) 4 x 2 y 2 + 9 z 2 + 8 x + 2 y + 18 z + 60 = 0 4. Use the Principal Axis Theorem to sketch the surface:
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Unformatted text preview: (a) 3 x 2 8 xy + 3 y 2 + z 2 = 1 (b) 17 x 2 12 xy + 8 y 2 + z 2 = 4 (c) 4 xz + 4 y 2 = 4 (d) 5 x 2 + 3 y 2 + 3 z 2 + 2 xy 2 xz 2 yz = 6...
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