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37. r(t) = (cos 2t, cos 3t, cos 4t)

37. r(t) = (cos 2t, cos 3t, cos 4t)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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37

ate 5, 1) r(t) = t²i+ In tj+ (1/t) k. 30. Find three different surfaces that contain the curve sect the paraboloid z = x² + y²? 31. At what points does the curve r(t) = ti+ (2t - 1²) k inter- the sphere x² + y² + z² = 5? 32. At what points does the helix r(t) = (sin t, cos t, t) intersect 33-37 Use a computer to graph the curve with the given vector equation. Make sure you choose a parameter domain and view- points that reveal the true nature of the curve. 33. r(t) = (cost sin 2t, sin t sin 2t, cos 2t) 34. r(t) = (te', e, t) 35. r(t) = (sin 3t cos t, 4t, sin 3t sin t) 36. r(t) = (cos(8 cos t) sin t, sin(8 cos t) sin t, cos t) 37. r(t) = (cos 2t, cos 3t, cos 4t) $6 38. Graph the curve with parametric equations x = sint, y = sin 2t, z = cos 4t. Explain its shape by graphing its projections onto the three coordinate planes. 39. Graph the curve with parametric equations x = (1 + cos 16t) cos t y = (1 + cos 16t) sin t z = 1 + cos 16t 2DA3X3 Explain the appearance of the graph by showing that it lies on a cone. 40. Graph the curve with parametric equations
Transcribed Image Text:ate 5, 1) r(t) = t²i+ In tj+ (1/t) k. 30. Find three different surfaces that contain the curve sect the paraboloid z = x² + y²? 31. At what points does the curve r(t) = ti+ (2t - 1²) k inter- the sphere x² + y² + z² = 5? 32. At what points does the helix r(t) = (sin t, cos t, t) intersect 33-37 Use a computer to graph the curve with the given vector equation. Make sure you choose a parameter domain and view- points that reveal the true nature of the curve. 33. r(t) = (cost sin 2t, sin t sin 2t, cos 2t) 34. r(t) = (te', e, t) 35. r(t) = (sin 3t cos t, 4t, sin 3t sin t) 36. r(t) = (cos(8 cos t) sin t, sin(8 cos t) sin t, cos t) 37. r(t) = (cos 2t, cos 3t, cos 4t) $6 38. Graph the curve with parametric equations x = sint, y = sin 2t, z = cos 4t. Explain its shape by graphing its projections onto the three coordinate planes. 39. Graph the curve with parametric equations x = (1 + cos 16t) cos t y = (1 + cos 16t) sin t z = 1 + cos 16t 2DA3X3 Explain the appearance of the graph by showing that it lies on a cone. 40. Graph the curve with parametric equations
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