Seção 13 2 R

Prévia do material em texto

2  SEÇÃO 13.2 DERIVADAS E INTEGRAIS DE FUNÇÕES VETORIAIS
 1. (a), (c)
(b) 3t2 , 2t
 2. (a), (c)
(b) et i − 2e− 2 t j
 3. (a), (c)
(b) sec t tg t i + sec2 t j
 4. �, r (t) = 1, 2t, 3t2
 5. {t | 4 ≤ t ≤ 6}, r (t) = 2t,
1
2 t − 4
,− 1
2 6 − t
 6. t | t ≠ (2n + 1) pi2 , n um inteiro ,
r (t) = sec2 t j + (sec t tg t) k
 7. {t | t ≠ −1}, r (t) = (1 + 2t) e2 t i+
2
(t + 1)2
j+ 1
1+ t2
k
 8. r (t) = −
2t
4 − t2
i + 1
2 1+ t
j − 12e3 t k
 9. r (t) = −e− t (cos t + sen t) i + e− t (cos t − sen t) j + 1
t
k
 10. 1
6 ,−
2
3 ,
1
6
 11. 25 i +
2 3
5 j −
3
5 k
 12. − 13 i +
2
3 j +
2
3 k
 13. 1
46 ,
3
46 ,
6
46
 14. 23 ,−
2
3 ,
1
3
 15. x = 1 + t , y = 1 + 2t , z = 1 + 3t
 16. x = 1 + 2t , y = 1 + t , z = 1 − t
 17. x = − pi2 t , y =
1
4 + t , z = 1 + 4t
 18. x = −pit , y = 1 + 12 t , z = −1
 19. x = pi4 + t , y = 1 − t , z = 1 + t
 20. x = 1, y = 3 + 6t , z = 3 − 6t
 21. 12 i +
1
3 j +
1
4 k
 22. 103 i −
124
5 j −
4
3 k
 23. 12 i +
1
2 j +
4− pi
4 2 k
13.2 RESPOSTAS Revisão técnica: Ricardo Miranda Martins – IMECC – Unicamp