exo7 5007

Déterminer les branches infinies pour les courbes paramétrées suivantes :

1

\(x=4t^5-4t^3+t\), \(y=\dfrac{t}{3t^4+1}\)

2

\(x=2\cos^2t+\ln|\sin t|\), \(y=\sin 2t\)

3

\(x=\sqrt{\dfrac{t^2-2}{t^4-1}}\), \(y=tx\)

4

\(x=\dfrac{t^3-t}{2t-1}\), \(y=tx\)

5

\(x=\dfrac1t+\dfrac1{t+1}\), \(y=\dfrac1t+\dfrac1{(t+1)^2}\)

6

\(x=\sin \dfrac t2\), \(y=\tan t\)

7

\(x=\dfrac1t+\dfrac1{t+1}\), \(y=\dfrac1t-\dfrac1{t+1}\)

8

\(x=\dfrac{3t}{1+t^3}\), \(y=tx\)

9

\(x=\dfrac{te^t}{t+1}\), \(y=\dfrac{e^t}{t+1}\)

10

\(x=2t^3+3t^2\), \(y=3t^2+6t\)

11

\(x=t^3-3t\),

12

\(x=\dfrac t{t^2-1}\), \(y=\dfrac{t^2}{t-1}\)