1 x 3 2 z 0 the figure 11 2z 6x y100 136 exercises 2 1

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Unformatted text preview: 2z2 k 1 yk (3, 1, 0) x FIGURE 11 ≈+2z@-6x-y+10=0 |||| 13.6 The trace in the xy-plane is the parabola with equation y paraboloid is sketched in Figure 11. x 2 represent as a curve in (b) What does it represent as a surface in 3 ? (c) What does the equation z y 2 represent? e x as a curve in 2. (b) Sketch the graph of y e x as a surface in 3. (c) Describe and sketch the surface z e y. 2. (a) Sketch the graph of y |||| 3. y 4. z 2 Describe and sketch the surface. 4z 2 4 x 3 2, z 0. The Exercises 1. (a) What does the equation y 3–8 1 4 x 2 2 y2 5. x ? 7. z ■ 6. yz 0 8. x cos x ■ ■ ■ ■ ■ ■ 2 ■ 4 y2 ■ 1 ■ ■ ■ 9. (a) Find and identify the traces of the quadric surface x 2 y 2 z 2 1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x 2 y 2 z 2 1, how is the graph affected? (c) What if we change the equation in part (a) to x 2 y 2 2 y z 2 0? 5E-13(pp 868-877) ❙❙❙❙ 874 1/18/06 11:37 AM Page 874 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE 10. (a) Find and identify the traces of the quadric surface 29–36 |||| Reduce the equation to one of the standard forms, classify the surface, and sketch it. x 2 y 2 z 2 1 and explain why the graph looks like the graph of the hyperboloid of two sheets in Table 1. (b) If the equation in part (a) is changed to x 2 y 2 z 2 1, what happens to the graph? Sketch the new graph. 11–20 y Find the traces of the given surface in the planes x k. Then identify the surface and sketch it. |||| k, z 11. 4 x 2 9y 2 13. y 2 15. x2 x2 36 z 2 x2 12. 4y 36 z2 4y 2 z2 k, z2 2 2 34. 4 y 4z2 z2 19. y ■ ■ y 18. x 2 0 x2 20. 16 x 2 ■ ■ ■ ■ ■ z2 y2 ■ y2 2 2 2 4 ■ ■ ■ |||| Match the equation with its graph (labeled I–VIII). Give reasons for your choices. 4y 2 9z 2 22. 9x 2 1 4y 2 z2 y2 z2 25. y 2x 2 z2 26. y 2 1 28. y 27. x 2 2z2 x2 24. 1 y2 z2 x2 x2 3x 2 37. z z 39. z 1 1 2 2 2 x ■ 4y ■ 0 ■ ■ 38. 8 x 2 40. z ■ and x 2 y2 ■...
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