TAILIEUCHUNG - Chapter 1: Vector functions

Chapter 1 vector functions include the contents: Vector functions and space curves, Derivatives and integrals of vector functions, Arc length and curvature, motion in space. | CHAPTER 1. VECTOR FUNCTIONS . Vector Functions and Space Curves 1-2 Find the domain of the vector function. 1. r D e 31 ln z 1 t - 2 A 2. r t 2 s n W9 3-6 Find the limit. t 3. lim e 3 i 9 i cos 2 k -0 sin2 J - I. f2 t - K . -a- . sin 7TÍ - 4. lim -- 7- Ỉ 4- Ự 8 j - k -1 Í - 1 J In t _ 11 t2 . 1 - e 2 5. lim ------T tan t ----------- 1 - t2 t Í3 t A 6. lim te T - sin 2Z3 1 t 7-14 Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. 7. r z sin t t 8. r z t2 9. r ộ 42 - t 2t 10. r z sin TTt t cos irt 11. r ộ 1 cos 4 2 sin t 12. r ộ 2i 4- ị 4- 2k 13. r í f i z4j 4- z6k 14. r z cos i cos j 4- sin k 15-16 Draw the projections of the curve on the three coordinate planes. Use these projections to help sketch the curve. 15. r 4 sin 4 2 cos z 16. r z 4 4 f2 17-20 Find a vector equation and parametric equations for the line segment that joins Pto Q. 17. H2 0 0 Ợ6 2 -2 18. Ạ-1 2 -2 ự-3 5 1 19. P 0 -1. 1 ọ I j 20. fía b c Q u V Ù 21-26 Match the parametric equations with the graphs labeled I-VI . Give reasons for your choices. 21. X 7cos 4 y t z sin 4 0 22. X cos 4 y sin 4 2 1 1 4- z2 23. x t y 1 1 4- t2 2 t2 24. X cos 4 y sin 4 z cos 2 25. A cos84 y sin84 2 eQAi Z 0 26. X cos2 4 y sin2 4 z t 27. Show that the curve with parametric equations X cos 4 y sin 4 z lies on the cone z2 X2 y2 and use this fact to help sketch the curve. 28. Show that the curve with parametric equations A sin 4 y cos 4 z sin2 is the curve of intersection of the surfaces z X2 and X2 4- y2 1. Use tills fact to help sketch the curve. 29. At what points does the curve r z zi 4- 2 t2 k intersect the paraboloid z X2 4- y2 30. At what points does the helix r z sin 4 cos 4 t intersect the sphere X2 4- y2 4- z2 5 31-35 Use a computer to graph the curve with the given vector equation. Make sure you choose a parameter domain and viewpoints that reveal the true nature of the curve. 31. r cos Zsin 24 sin sin 24 cos 2f 32. r z 2 In 4 z 33. r Z 4 Zsin 4 tcos z .

• Toán học
• Chapter 1 vector functions
• Vector functions and space curves
• Derivatives and integrals of vector functions
• Arc length and curvature
• Motion in space
• Tóm tắt Đồ án tốt nghiệp
• Đồ án tốt nghiệp Truyền thông đa phương tiện
• Truyền thông đa phương tiện
• Hoạt hình Motion Graphic
• Xây dựng đoạn phim motion Life Of Future
• Space flight dynamics
• Non keplerian motion
• Rocket performance
• Orbit determination
• Time of flight
• Relative motion and orbital rendezvous
• Low thrust transfers
• Interplanetary trajectories
• Atmospheric entry
• Configuration space
• ordinary differential
• generalized coordinate
• the forces entering
• dynamic equilibrium
• generic function
• báo cáo khoa học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• báo cáo y học
• công trình nghiên cứu về y học
• tài liệu về y học
• Computational geometry
• Delaunay triangulations
• More geometric data structures
• Convex hulls
• Binary space partitions
• Robot motion planning
• BMC Geriatrics
• Life space
• Motion sensors
• Potential mobility determinants
• Real life mobility
• Potential Fields
• Obstacle Avoidance
• Reading Robot
• Mobile Robots
• Rewarded Goal
• Intelligent Space
• An introduction to the visual system
• The visual system
• Colour constancy
• Object perception and recognition
• Face recognition
• Motion perception
• Brain and space