cours 4
1.4 LONGUEUR
D’ARC ET ABSCISSE
CURVILIGNE
Au dernier cours, nous avons vu
Au dernier cours, nous avons vu
Dérivées de fonctions vectorielles.
Au dernier cours, nous avons vu
Dérivées de fonctions vectorielles.
Règles de dérivation.
Au dernier cours, nous avons vu
Dérivées de fonctions vectorielles.
Règles de dérivation.
Vecteur tangent unitaire.
Aujourd’hui, nous allons voir
Aujourd’hui, nous allons voir
Intégrale d’une fonction vectorielle
Aujourd’hui, nous allons voir
Intégrale d’une fonction vectorielle La longueur d’une courbe
Aujourd’hui, nous allons voir
Intégrale d’une fonction vectorielle La longueur d’une courbe
L’abscisse curviligne
Aujourd’hui, nous allons voir
Intégrale d’une fonction vectorielle La longueur d’une courbe
L’abscisse curviligne Repère de Frenet
L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit> 3
L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit> 3
OP<latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit> ~ = OA~ + kd~
Donc l’équation de la droite tangente à la courbe est L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit> 3
OP<latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">AAAC3nicjVHLSsNAFD2Nr1pfUVfiJlgEQSipCLoRqm7cWcE+oC01mU41NE1CMimUUty5E7f+gFv9HPEP9C+8M01BLaITkpw5954zc++1A9eJhGm+pbSp6ZnZufR8ZmFxaXlFX10rR34cMl5ivuuHVduKuOt4vCQc4fJqEHKra7u8YndOZbzS42Hk+N6l6Ae80bWuPaftMEsQ1dQ36j3OBufF4dEIHA93OxIZraaeNXOmWsYkyCcgi2QVff0VdbTggyFGFxweBGEXFiJ6asjDREBcAwPiQkKOinMMkSFtTFmcMixiO/S9pl0tYT3aS89IqRmd4tIbktLANml8ygsJy9MMFY+Vs2R/8x4oT3m3Pv3txKtLrMANsX/pxpn/1claBNo4VDU4VFOgGFkdS1xi1RV5c+NLVYIcAuIkblE8JMyUctxnQ2kiVbvsraXi7ypTsnLPktwYH/KWNOD8z3FOgvJeLk/4Yj9bOElGncYmtrBD8zxAAWcookTet3jCM160K+1Ou9ceRqlaKtGs49vSHj8B456Zag==</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">AAAC3nicjVHLSsNAFD2Nr1pfUVfiJlgEQSipCLoRqm7cWcE+oC01mU41NE1CMimUUty5E7f+gFv9HPEP9C+8M01BLaITkpw5954zc++1A9eJhGm+pbSp6ZnZufR8ZmFxaXlFX10rR34cMl5ivuuHVduKuOt4vCQc4fJqEHKra7u8YndOZbzS42Hk+N6l6Ae80bWuPaftMEsQ1dQ36j3OBufF4dEIHA93OxIZraaeNXOmWsYkyCcgi2QVff0VdbTggyFGFxweBGEXFiJ6asjDREBcAwPiQkKOinMMkSFtTFmcMixiO/S9pl0tYT3aS89IqRmd4tIbktLANml8ygsJy9MMFY+Vs2R/8x4oT3m3Pv3txKtLrMANsX/pxpn/1claBNo4VDU4VFOgGFkdS1xi1RV5c+NLVYIcAuIkblE8JMyUctxnQ2kiVbvsraXi7ypTsnLPktwYH/KWNOD8z3FOgvJeLk/4Yj9bOElGncYmtrBD8zxAAWcookTet3jCM160K+1Ou9ceRqlaKtGs49vSHj8B456Zag==</latexit> ~ = OA~ + kd~
Donc l’équation de la droite tangente à la courbe est L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">AAACznicjVHLSsNAFD2Nr1pfVZdugkVwVRIVdFl047KKfUBbZZJO26F5kUwKpRS3/oBb/SzxD/QvvDOmoBbRCUnOnHvOnbn3OpEnEmlZrzljYXFpeSW/Wlhb39jcKm7v1JMwjV1ec0MvjJsOS7gnAl6TQnq8GcWc+Y7HG87wQsUbIx4nIgxu5DjiHZ/1A9ETLpNEtdo+kwPHMa9vj++KJats6WXOAzsDJWSrGhZf0EYXIVyk8MERQBL2wJDQ04INCxFxHUyIiwkJHeeYokDelFScFIzYIX37tGtlbEB7lTPRbpdO8eiNyWnigDwh6WLC6jRTx1OdWbG/5Z7onOpuY/o7WS6fWIkBsX/5Zsr/+lQtEj2c6RoE1RRpRlXnZllS3RV1c/NLVZIyRMQp3KV4TNjVzlmfTe1JdO2qt0zH37RSsWrvZtoU7+qWNGD75zjnQf2obBO+OilVzrNR57GHfRzSPE9RwSWqqOmOP+IJz0bVGBlT4/5TauQyzy6+LePhA+REkzY=</latexit> 3
OP<latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit> ~ = OA~ + kd~
OP<latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit> ~ = ~r(a) + k~r 0(a)
Donc l’équation de la droite tangente à la courbe est L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit> 3
OP<latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">AAAC3nicjVHLSsNAFD2Nr1pfUVfiJlgEQSipCLoRqm7cWcE+oC01mU41NE1CMimUUty5E7f+gFv9HPEP9C+8M01BLaITkpw5954zc++1A9eJhGm+pbSp6ZnZufR8ZmFxaXlFX10rR34cMl5ivuuHVduKuOt4vCQc4fJqEHKra7u8YndOZbzS42Hk+N6l6Ae80bWuPaftMEsQ1dQ36j3OBufF4dEIHA93OxIZraaeNXOmWsYkyCcgi2QVff0VdbTggyFGFxweBGEXFiJ6asjDREBcAwPiQkKOinMMkSFtTFmcMixiO/S9pl0tYT3aS89IqRmd4tIbktLANml8ygsJy9MMFY+Vs2R/8x4oT3m3Pv3txKtLrMANsX/pxpn/1claBNo4VDU4VFOgGFkdS1xi1RV5c+NLVYIcAuIkblE8JMyUctxnQ2kiVbvsraXi7ypTsnLPktwYH/KWNOD8z3FOgvJeLk/4Yj9bOElGncYmtrBD8zxAAWcookTet3jCM160K+1Ou9ceRqlaKtGs49vSHj8B456Zag==</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit> ~ = OA~ + kd~
OP<latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">AAAC5XicjVHLSsNAFD3GV31XXboJFrEiSCqCboSiG3dWsFawUibTsYamSZhMClLcunMnbv0Bt/or4h/oX3hnnIJaRCckOffce87MnesnYZAqz3sdcoZHRsfGcxOTU9Mzs3P5+YWTNM4kF1Ueh7E89VkqwiASVRWoUJwmUrCOH4qa397X+VpXyDSIo2N1lYjzDmtFwUXAmSKqkXfrXcF7h5XrXQ1cWWRr6+1PWHdXKWrkC96GZ5Y7CEoWFGBXJc6/oI4mYnBk6EAggiIcgiGl5wwleEiIO0ePOEkoMHmBa0ySNqMqQRWM2DZ9WxSdWTaiWHumRs1pl5BeSUoXK6SJqU4S1ru5Jp8ZZ83+5t0znvpsV/T3rVeHWIVLYv/S9Sv/q9O9KFxgx/QQUE+JYXR33Lpk5lb0yd0vXSlySIjTuEl5SZgbZf+eXaNJTe/6bpnJv5lKzeqY29oM7/qUNODSz3EOgpPNjRLho61Cec+OOoclLKNI89xGGQeooEreN3jEE56dlnPr3Dn3n6XOkNUs4ttyHj4A1PKazw==</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit> ~ = ~r(a) + k~r 0(a)
Donc l’équation de la droite tangente à la courbe est L’équation vectorielle d’une droite dans estR<latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit><latexit sha1_base64="Doqolex/8a6hKe+63cyWJs+DIos=">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</latexit> 3
OP<latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">AAAC3nicjVHLSsNAFD2Nr1pfUVfiJlgEQSipCLoRqm7cWcE+oC01mU41NE1CMimUUty5E7f+gFv9HPEP9C+8M01BLaITkpw5954zc++1A9eJhGm+pbSp6ZnZufR8ZmFxaXlFX10rR34cMl5ivuuHVduKuOt4vCQc4fJqEHKra7u8YndOZbzS42Hk+N6l6Ae80bWuPaftMEsQ1dQ36j3OBufF4dEIHA93OxIZraaeNXOmWsYkyCcgi2QVff0VdbTggyFGFxweBGEXFiJ6asjDREBcAwPiQkKOinMMkSFtTFmcMixiO/S9pl0tYT3aS89IqRmd4tIbktLANml8ygsJy9MMFY+Vs2R/8x4oT3m3Pv3txKtLrMANsX/pxpn/1claBNo4VDU4VFOgGFkdS1xi1RV5c+NLVYIcAuIkblE8JMyUctxnQ2kiVbvsraXi7ypTsnLPktwYH/KWNOD8z3FOgvJeLk/4Yj9bOElGncYmtrBD8zxAAWcookTet3jCM160K+1Ou9ceRqlaKtGs49vSHj8B456Zag==</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">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</latexit><latexit sha1_base64="H7S79+DVJ4RsGB/Xhn3Nm3zQpWE=">AAAC3nicjVHLSsNAFD2Nr1pfUVfiJlgEQSipCLoRqm7cWcE+oC01mU41NE1CMimUUty5E7f+gFv9HPEP9C+8M01BLaITkpw5954zc++1A9eJhGm+pbSp6ZnZufR8ZmFxaXlFX10rR34cMl5ivuuHVduKuOt4vCQc4fJqEHKra7u8YndOZbzS42Hk+N6l6Ae80bWuPaftMEsQ1dQ36j3OBufF4dEIHA93OxIZraaeNXOmWsYkyCcgi2QVff0VdbTggyFGFxweBGEXFiJ6asjDREBcAwPiQkKOinMMkSFtTFmcMixiO/S9pl0tYT3aS89IqRmd4tIbktLANml8ygsJy9MMFY+Vs2R/8x4oT3m3Pv3txKtLrMANsX/pxpn/1claBNo4VDU4VFOgGFkdS1xi1RV5c+NLVYIcAuIkblE8JMyUctxnQ2kiVbvsraXi7ypTsnLPktwYH/KWNOD8z3FOgvJeLk/4Yj9bOElGncYmtrBD8zxAAWcookTet3jCM160K+1Ou9ceRqlaKtGs49vSHj8B456Zag==</latexit> ~ = OA~ + kd~
OP<latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit><latexit sha1_base64="2Awddmdbya/AE8AnkIfNJhpxk24=">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</latexit> ~ = ~r(a) + k~r 0(a)
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">AAAC43icjVHLSgQxECzH1/pe9ShIcBFWEJkVQS+C6MXjCu4qOCIzMWpwXiQZYRFv3ryJV3/Aq/6L+Af6F3biLPhANMMklequSjod5bHUxvdferzevv6BwcrQ8Mjo2PhEdXKqrbNCcdHiWZyp/SjUIpapaBlpYrGfKxEmUSz2ovMtG9+7EErLLN01nVwcJuFpKk8kDw1RR9XZ4EJwpupmYZ3VA55pZhZZoGVqV7NwVK35S74b7CdolKCGcjSz6jMCHCMDR4EEAikM4RghNH0HaMBHTtwhLolThKSLC1xhmLQFZQnKCIk9p/mUdgclm9Leemqn5nRKTL8iJcM8aTLKU4TtaczFC+ds2d+8L52nvVuH1qj0Sog1OCP2L1038786W4vBCdZcDZJqyh1jq+OlS+Fexd6cfarKkENOnMXHFFeEuVN235k5jXa127cNXfzVZVrW7nmZW+DN3pIa3Pjezp+gvbzUILyzUtvYLFtdwQzmUKd+rmID22iiRd7XeMAjnjzh3Xi33t1HqtdTaqbxZXj371NumXI=</latexit>
Hélice
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit>
Hélice
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">AAAC43icjVHLSgQxECzH1/pe9ShIcBFWEJkVQS+C6MXjCu4qOCIzMWpwXiQZYRFv3ryJV3/Aq/6L+Af6F3biLPhANMMklequSjod5bHUxvdferzevv6BwcrQ8Mjo2PhEdXKqrbNCcdHiWZyp/SjUIpapaBlpYrGfKxEmUSz2ovMtG9+7EErLLN01nVwcJuFpKk8kDw1RR9XZ4EJwpupmYZ3VA55pZhZZoGVqV7NwVK35S74b7CdolKCGcjSz6jMCHCMDR4EEAikM4RghNH0HaMBHTtwhLolThKSLC1xhmLQFZQnKCIk9p/mUdgclm9Leemqn5nRKTL8iJcM8aTLKU4TtaczFC+ds2d+8L52nvVuH1qj0Sog1OCP2L1038786W4vBCdZcDZJqyh1jq+OlS+Fexd6cfarKkENOnMXHFFeEuVN235k5jXa127cNXfzVZVrW7nmZW+DN3pIa3Pjezp+gvbzUILyzUtvYLFtdwQzmUKd+rmID22iiRd7XeMAjnjzh3Xi33t1HqtdTaqbxZXj371NumXI=</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">AAAC43icjVHLSgQxECzH1/pe9ShIcBFWEJkVQS+C6MXjCu4qOCIzMWpwXiQZYRFv3ryJV3/Aq/6L+Af6F3biLPhANMMklequSjod5bHUxvdferzevv6BwcrQ8Mjo2PhEdXKqrbNCcdHiWZyp/SjUIpapaBlpYrGfKxEmUSz2ovMtG9+7EErLLN01nVwcJuFpKk8kDw1RR9XZ4EJwpupmYZ3VA55pZhZZoGVqV7NwVK35S74b7CdolKCGcjSz6jMCHCMDR4EEAikM4RghNH0HaMBHTtwhLolThKSLC1xhmLQFZQnKCIk9p/mUdgclm9Leemqn5nRKTL8iJcM8aTLKU4TtaczFC+ds2d+8L52nvVuH1qj0Sog1OCP2L1038786W4vBCdZcDZJqyh1jq+OlS+Fexd6cfarKkENOnMXHFFeEuVN235k5jXa127cNXfzVZVrW7nmZW+DN3pIa3Pjezp+gvbzUILyzUtvYLFtdwQzmUKd+rmID22iiRd7XeMAjnjzh3Xi33t1HqtdTaqbxZXj371NumXI=</latexit>
Hélice
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit>
Hélice
~r 0(t) = ( sin t, cos t, 1)
<latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">AAAC53icjVHLSsQwFD3W93vUpZvgII6g0oqgG0F041LBcQQrQxujBjttSVJBxL07d+LWH3CrfyL+gf6FN7ED6iCa0uTk3HtOcnPjPJHa+P5rl9fd09vXPzA4NDwyOjZemZjc11mhuKjzLMnUQRxpkchU1I00iTjIlYhacSIa8fmWjTcuhNIyS/fMZS6OWtFpKk8kjwxRzcpMeCE4UyGbq5n5dVZbDLVMmVlgIc+0XYP5ZqXqL/lusE4QlKCKcuxklReEOEYGjgItCKQwhBNE0PQdIoCPnLgjXBGnCEkXF7jGEGkLyhKUERF7TvMp7Q5LNqW99dROzemUhH5FSoZZ0mSUpwjb05iLF87Zsr95XzlPe7dLWuPSq0WswRmxf+namf/V2VoMTrDmapBUU+4YWx0vXQr3Kvbm7EtVhhxy4iw+prgizJ2y/c7MabSr3b5t5OJvLtOyds/L3ALv9pbU4OBnOzvB/vJSQHh3pbqxWbZ6ANOYQY36uYoNbGMHdfK+wSOe8OxJ79a78+4/U72uUjOFb8N7+ABYqJon</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit>
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit>
Hélice
~r 0(t) = ( sin t, cos t, 1)
<latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit>
L’équation de la droite tangente en t = ⇡ 2
<latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit>
Exemple
~r(t) = (cos t, sin t, t)<latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">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</latexit><latexit sha1_base64="jwisrcU9OPLyYxt5s5F2mO2Uf7M=">AAAC43icjVHLSgQxECzH1/pe9ShIcBFWEJkVQS+C6MXjCu4qOCIzMWpwXiQZYRFv3ryJV3/Aq/6L+Af6F3biLPhANMMklequSjod5bHUxvdferzevv6BwcrQ8Mjo2PhEdXKqrbNCcdHiWZyp/SjUIpapaBlpYrGfKxEmUSz2ovMtG9+7EErLLN01nVwcJuFpKk8kDw1RR9XZ4EJwpupmYZ3VA55pZhZZoGVqV7NwVK35S74b7CdolKCGcjSz6jMCHCMDR4EEAikM4RghNH0HaMBHTtwhLolThKSLC1xhmLQFZQnKCIk9p/mUdgclm9Leemqn5nRKTL8iJcM8aTLKU4TtaczFC+ds2d+8L52nvVuH1qj0Sog1OCP2L1038786W4vBCdZcDZJqyh1jq+OlS+Fexd6cfarKkENOnMXHFFeEuVN235k5jXa127cNXfzVZVrW7nmZW+DN3pIa3Pjezp+gvbzUILyzUtvYLFtdwQzmUKd+rmID22iiRd7XeMAjnjzh3Xi33t1HqtdTaqbxZXj371NumXI=</latexit>
Hélice
~r 0(t) = ( sin t, cos t, 1)
<latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">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</latexit><latexit sha1_base64="0wY6ZdrYcbBArjxxHGcLFlixpBg=">AAAC53icjVHLSsQwFD3W93vUpZvgII6g0oqgG0F041LBcQQrQxujBjttSVJBxL07d+LWH3CrfyL+gf6FN7ED6iCa0uTk3HtOcnPjPJHa+P5rl9fd09vXPzA4NDwyOjZemZjc11mhuKjzLMnUQRxpkchU1I00iTjIlYhacSIa8fmWjTcuhNIyS/fMZS6OWtFpKk8kjwxRzcpMeCE4UyGbq5n5dVZbDLVMmVlgIc+0XYP5ZqXqL/lusE4QlKCKcuxklReEOEYGjgItCKQwhBNE0PQdIoCPnLgjXBGnCEkXF7jGEGkLyhKUERF7TvMp7Q5LNqW99dROzemUhH5FSoZZ0mSUpwjb05iLF87Zsr95XzlPe7dLWuPSq0WswRmxf+namf/V2VoMTrDmapBUU+4YWx0vXQr3Kvbm7EtVhhxy4iw+prgizJ2y/c7MabSr3b5t5OJvLtOyds/L3ALv9pbU4OBnOzvB/vJSQHh3pbqxWbZ6ANOYQY36uYoNbGMHdfK+wSOe8OxJ79a78+4/U72uUjOFb8N7+ABYqJon</latexit>
L’équation de la droite tangente en t = ⇡ 2
<latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit><latexit sha1_base64="3ASt+duuIALJRaEvrIn1Bd+KmsA=">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</latexit>
(x, y, z) = ~r ⇣ ⇡ 2
⌘ + k~r 0 ⇣ ⇡ 2
⌘
<latexit sha1_base64="cKDpCtPH3w7ty8LgMp0hhLbvPuw=">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</latexit><latexit sha1_base64="cKDpCtPH3w7ty8LgMp0hhLbvPuw=">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</latexit><latexit sha1_base64="cKDpCtPH3w7ty8LgMp0hhLbvPuw=">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</latexit><latexit sha1_base64="cKDpCtPH3w7ty8LgMp0hhLbvPuw=">AAADFXicjVFBSxtBGH1ubbVq29geexkMYkJFNqGgF0Hai8cIRgU3hN3JJBmy2V1mZ4Mx5Hf4T3rrrfTaowheW/Rf+M04QquEOsvuvnnfe2/mm4myWOba96/mvBfzL18tLL5eWl558/ZdafX9UZ4WiosmT+NUnURhLmKZiKaWOhYnmRLhMIrFcTT4aurHI6FymSaHepyJ1jDsJbIreaiJapcalbNNNt5k59VdFowEZyqIRVdXgq4K+STI5HRSnwZK9vq6+mngFGxjtqhdKvtbvh3sKag5UIYbjbR0iQAdpOAoMIRAAk04RoicnlPU4CMjroUJcYqQtHWBKZbIW5BKkCIkdkDfHs1OHZvQ3GTm1s1plZheRU6GdfKkpFOEzWrM1gubbNhZ2RObafY2pn/ksobEavSJ/Z/vQflcn+lFo4sd24OknjLLmO64SynsqZids7+60pSQEWdwh+qKMLfOh3Nm1pPb3s3ZhrZ+Y5WGNXPutAVuzS7pgmuPr/MpOKpv1QgffC7vfXFXvYiPWEOF7nMbe9hHA03K/oZr/MYf78L77v3wft5LvTnn+YB/hvfrDprHrtA=</latexit>