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5. x = cos 2t, y = sin 2t, 0

5. x = cos 2t, y = sin 2t, 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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21:16 " 39 บทที่1สมการอิงตัวแปร -1 - -sin -1 -sin А В (-sin1 y This is precisely the time it takes amount of time to reach B no mat FIGURE 11.11 Beads released simultaneously on the upside-down cycloid A, and C in Figure 11.11, for inst that Huygens' pendulum clock is at O, A, and C will reach B at the same time. Exercises 11.1 Finding Cartesian from Parametric Equations Exercises 1–18 give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. (The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion. 15. х 16. х 17. х 18. х Findin 1. x = 3t, y = 9t², -∞ < t < ∞ 19. Fir - Vt, y = t, t>0 3. х %3D 2t — 5, у %3D 4t — 7, -со <t< x0 4. x = 3 – 3t, y = 2t, 0 <t < 1 2. x = of а. с. 5. x = cos 2t, y = sin 2t, 0 <t<™ 6. x = cos (п — t), у %3D sin (п — t), 0<isп th || 7. x = 4 cos t, y = 2 sin t, 0<t< 2m 8. x = 4 sin t, y 20. Fir 5 cos t, 0 < t< 2m of (x 9. х %— sin t, y = cos 2t, а. 10. x = 1 + sin t, y = cos t 2, 0 <t< с. 11. x = t², y = 16 – 21“, - 00 < t < (A t - 2 v = 1’ 12. x = -1 < t< 1 t + 1’ In Exe: f - V1 – ², Vt + 1, y = Vi, t> 0 13. х —D t, y = -1 <t< 0 21. the 14. х — 22. the 7 จาก 50 +)
Transcribed Image Text:21:16 " 39 บทที่1สมการอิงตัวแปร -1 - -sin -1 -sin А В (-sin1 y This is precisely the time it takes amount of time to reach B no mat FIGURE 11.11 Beads released simultaneously on the upside-down cycloid A, and C in Figure 11.11, for inst that Huygens' pendulum clock is at O, A, and C will reach B at the same time. Exercises 11.1 Finding Cartesian from Parametric Equations Exercises 1–18 give parametric equations and parameter intervals for the motion of a particle in the xy-plane. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. (The graphs will vary with the equation used.) Indicate the portion of the graph traced by the particle and the direction of motion. 15. х 16. х 17. х 18. х Findin 1. x = 3t, y = 9t², -∞ < t < ∞ 19. Fir - Vt, y = t, t>0 3. х %3D 2t — 5, у %3D 4t — 7, -со <t< x0 4. x = 3 – 3t, y = 2t, 0 <t < 1 2. x = of а. с. 5. x = cos 2t, y = sin 2t, 0 <t<™ 6. x = cos (п — t), у %3D sin (п — t), 0<isп th || 7. x = 4 cos t, y = 2 sin t, 0<t< 2m 8. x = 4 sin t, y 20. Fir 5 cos t, 0 < t< 2m of (x 9. х %— sin t, y = cos 2t, а. 10. x = 1 + sin t, y = cos t 2, 0 <t< с. 11. x = t², y = 16 – 21“, - 00 < t < (A t - 2 v = 1’ 12. x = -1 < t< 1 t + 1’ In Exe: f - V1 – ², Vt + 1, y = Vi, t> 0 13. х —D t, y = -1 <t< 0 21. the 14. х — 22. the 7 จาก 50 +)
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