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