9. f(x, y) = 3x – 7y, r(t) = (cos t, sin t), t = 0 10. f(x, у) — 2х + 3у, r(t) — (3, г2), 13D -2 11. f(*, y) 3D х? - 3ху, г() — (сos t, sin r), 1%3D0 12. f(x, y) = x? – 3xy, r(t) = (cos t, sin t), %3D 13. fx, y) 3 sin(ху), r0) — (е", е%"). г—D0 14. f(x, у) 3 сos(y — х), r() 3 (e', е"), 1%3DIn3 15. f(x, у) 3Dх — ху, r() — (?, г2— 41), г34 16. F(x, y) — Зхе-, г() — (2г?, г2 — 2г). г—0 17. f(x, y) = Inx + In y, r(t)= (cos t,1²), t = %3D 18. g(x, y, z) = xye², r(t)= (1²,r³,t – 1), 1= 1 19. g(x, у, 2) %— хуг1, rt) — (e',t,1?), г%3D1 20. g(x, y, z, w) = x +2y + 3z + 5w, r(t)=(1²,r³, 1,t – 2), t=1 In Exercises 21–30, calculate the directional derivative in the direction of v at the given point. Remember to use a unit vector in your directional derivative computation. Activate Window

9. f(x, y) = 3x – 7y, r(t) = (cos t, sin t), t = 0 10. f(x, у) — 2х + 3у, r(t) — (3, г2), 13D -2 11. f(*, y) 3D х? - 3ху, г() — (сos t, sin r), 1%3D0 12. f(x, y) = x? – 3xy, r(t) = (cos t, sin t), %3D 13. fx, y) 3 sin(ху), r0) — (е", е%"). г—D0 14. f(x, у) 3 сos(y — х), r() 3 (e', е"), 1%3DIn3 15. f(x, у) 3Dх — ху, r() — (?, г2— 41), г34 16. F(x, y) — Зхе-, г() — (2г?, г2 — 2г). г—0 17. f(x, y) = Inx + In y, r(t)= (cos t,1²), t = %3D 18. g(x, y, z) = xye², r(t)= (1²,r³,t – 1), 1= 1 19. g(x, у, 2) %— хуг1, rt) — (e',t,1?), г%3D1 20. g(x, y, z, w) = x +2y + 3z + 5w, r(t)=(1²,r³, 1,t – 2), t=1 In Exercises 21–30, calculate the directional derivative in the direction of v at the given point. Remember to use a unit vector in your directional derivative computation. Activate Window

Name: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the va
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Description: In Exercises 9-20, use the Chain Rule to calculate - f(r(t)) at the value dt of t given. 9. f(x, y) = 3x – 7y, r(t) = (cos t, sin t), t = 010. f(x, у) — 2х + 3у, r(t) — (3, г2), 13D -211. f(*, y) 3D х? - 3ху, г() — (сos t, sin r), 1%3D012. f(x, y) =

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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