Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

10 D PARAMETRIC EQUATIONS AND POLAR COORDINATES
10.1 Curves Defined by Parametric Equations
1. X= t 2 + t, y = t 2 - t, -2 S t S 2
t - 2 - 1 0 l 2
X 2 0 0 2 6
y 6 2 0 0 2
y
t = - 2
(2, 6)
X
3. x = cos 2 t, y = 1 - sin t, 0 S t S 7r /2
t 0 7r/6 7r/3 7r/ 2
X 1 3/ 4 1/ 4 0
y 1 1/ 2 1 - 1 ~ 0.13 0
y
r=JI.
6
t=O
(1, 1)
X
5. X = 3 - 4t, y = 2 - 3t
(a)
t - 1 0 1 2
X 7 3 -1 - 5
y 5 2 -1 - 4
y
(7, S)
t= -1
(3, 2)
t = O
X
(b) X= 3 - 4t =} 4t = -X + 3 =} t = -~ X +~ ' SO
y = 2 - 3t = 2 - 3(- ~x + ~ ) = 2 +~ X - £ =} y =~X - ~
(-5, - 4)
1=2
1. x = 1 - e, v = t - 2, - 2 s t s 2
(- 3, 0)
t=2
y
(a)
t - 2 - 1 0 1 2
X -3 0 1 0 -3
y - 4 -3 - 2 - 1 0
X
(1, - 2)
t= O
(b) y = t - 2 =} t = y + 2, SO X= 1 - t 2 = 1 - (y + 2? =}
x = - (y + 2) 2 + 1, or x =:= - y 2 - 4y -e 3, with - 4 S y S 0
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