Solução_Calculo_Stewart_6e

F.
TX.10
10 PARAMETRIC EQUATIONS AND POLAR COORDINATES
10.1 Curves Defined by Parametric Equations
1. x =1+ √ t, y = t 2 − 4t, 0 ≤ t ≤ 5
t 0 1 2 3 4 5
x 1 2 1+ √ 2
2.41
1+ √ 3
2.73
3 1+ √ 5
3.24
y 0 −3 −4 −3 0 5
3. x =5sint, y = t 2 , −π ≤ t ≤ π
t −π −π/2 0 π/2 π
x 0 −5 0 5 0
y π 2 π 2 /4 0 π 2 /4
9.87 2.47 2.47
π 2
9.87
5. x =3t − 5, y =2t +1
(a)
t −2 −1 0 1 2 3 4
x −11 −8 −5 −2 1 4 7
y −3 −1 1 3 5 7 9
(b) x =3t − 5 ⇒ 3t = x +5 ⇒ t = 1 (x +5) ⇒
3
y =2· 1
3 (x +5)+1,soy = 2 3 x + 13 3 .
7. x = t 2 − 2, y =5− 2t, −3 ≤ t ≤ 4
(a)
t −3 −2 −1 0 1 2 3 4
x 7 2 −1 −2 −1 2 7 14
y 11 9 7 5 3 1 −1 −3
(b) y =5− 2t ⇒ 2t =5− y ⇒ t = 1 2
(5 − y) ⇒
x = 1
2 (5 − y)2 − 2,sox = 1 4 (5 − y)2 − 2, −3 ≤ y ≤ 11.
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