cours 2
1.2 FONCTIONS
VECTORIELLES, COURBES
ET SURFACES
Au dernier cours, nous avons vu
Au dernier cours, nous avons vu
Survol des cours calcul différentiel, calcul intégral et
algèbre linéaire.
Au dernier cours, nous avons vu
Survol des cours calcul différentiel, calcul intégral et algèbre linéaire.
Introduction des idées que nous verrons cette session.
Aujourd’hui, nous allons voir
Aujourd’hui, nous allons voir
Fonctions vectorielles
Aujourd’hui, nous allons voir
Fonctions vectorielles
Comment les visualiser
Aujourd’hui, nous allons voir
Fonctions vectorielles
Comment les visualiser
Limite
Aujourd’hui, nous allons voir
Fonctions vectorielles Comment les visualiser Limite
Surfaces paramétrées
On a déjà vu les fonctions de la forme
On a déjà vu les fonctions de la forme
f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
x 7 ! f (x)
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
x 7 ! f (x) = y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">AAAC1nicjVHLSsNAFD2Nr1pfqS7dBItQNyURQZdFNy4r2Ae0pSTptAaTTEgm2lJ0J279Abf6SeIf6F94Z0xBLaITkpw5954zc+91It9LhGm+5rS5+YXFpfxyYWV1bX1DL242Ep7GLqu73Odxy7ET5nshqwtP+KwVxcwOHJ81ncsTGW9esTjxeHguxhHrBvYw9Aaeawuienpx1PF5OAzsKBHcGJRHez29ZFZMtYxZYGWghGzVuP6CDvrgcJEiAEMIQdiHjYSeNiyYiIjrYkJcTMhTcYYbFEibUhajDJvYS/oOadfO2JD20jNRapdO8emNSWlglzSc8mLC8jRDxVPlLNnfvCfKU95tTH8n8wqIFbgg9i/dNPO/OlmLwABHqgaPaooUI6tzM5dUdUXe3PhSlSCHiDiJ+xSPCbtKOe2zoTSJql321lbxN5UpWbl3s9wU7/KWNGDr5zhnQWO/YpkV6+ygVD3ORp3HNnZQpnkeoopT1FAn72s84gnPWku71e60+89ULZdptvBtaQ8fqvOWPQ==</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit>7 ! f (x)
Aujourd’hui nous allons explorer les fonctions vectorielles.
=
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
~ r : R ! R
2x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">AAAC1nicjVHLSsNAFD2Nr1pfqS7dBItQNyURQZdFNy4r2Ae0pSTptAaTTEgm2lJ0J279Abf6SeIf6F94Z0xBLaITkpw5954zc+91It9LhGm+5rS5+YXFpfxyYWV1bX1DL242Ep7GLqu73Odxy7ET5nshqwtP+KwVxcwOHJ81ncsTGW9esTjxeHguxhHrBvYw9Aaeawuienpx1PF5OAzsKBHcGJRHez29ZFZMtYxZYGWghGzVuP6CDvrgcJEiAEMIQdiHjYSeNiyYiIjrYkJcTMhTcYYbFEibUhajDJvYS/oOadfO2JD20jNRapdO8emNSWlglzSc8mLC8jRDxVPlLNnfvCfKU95tTH8n8wqIFbgg9i/dNPO/OlmLwABHqgaPaooUI6tzM5dUdUXe3PhSlSCHiDiJ+xSPCbtKOe2zoTSJql321lbxN5UpWbl3s9wU7/KWNGDr5zhnQWO/YpkV6+ygVD3ORp3HNnZQpnkeoopT1FAn72s84gnPWku71e60+89ULZdptvBtaQ8fqvOWPQ==</latexit>7 ! f (x)
Aujourd’hui nous allons explorer les fonctions vectorielles.
=
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
~ r
<latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit>: R ! R
2x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">AAAC1nicjVHLSsNAFD2Nr1pfqS7dBItQNyURQZdFNy4r2Ae0pSTptAaTTEgm2lJ0J279Abf6SeIf6F94Z0xBLaITkpw5954zc+91It9LhGm+5rS5+YXFpfxyYWV1bX1DL242Ep7GLqu73Odxy7ET5nshqwtP+KwVxcwOHJ81ncsTGW9esTjxeHguxhHrBvYw9Aaeawuienpx1PF5OAzsKBHcGJRHez29ZFZMtYxZYGWghGzVuP6CDvrgcJEiAEMIQdiHjYSeNiyYiIjrYkJcTMhTcYYbFEibUhajDJvYS/oOadfO2JD20jNRapdO8emNSWlglzSc8mLC8jRDxVPlLNnfvCfKU95tTH8n8wqIFbgg9i/dNPO/OlmLwABHqgaPaooUI6tzM5dUdUXe3PhSlSCHiDiJ+xSPCbtKOe2zoTSJql321lbxN5UpWbl3s9wU7/KWNGDr5zhnQWO/YpkV6+ygVD3ORp3HNnZQpnkeoopT1FAn72s84gnPWku71e60+89ULZdptvBtaQ8fqvOWPQ==</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit>7 ! f (x)
t 7 ! ~ r(t)
Aujourd’hui nous allons explorer les fonctions vectorielles.
=
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
~ r
<latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">AAAC8HicjVHLSsQwFD3W93vUpZviIAjC0IqguBp041LFUcFRSWOcCbZNSVNFxI9w507c+gNu9SvEP9C/8CZW8YFoStuTc+85yb03ymKZmyB46vA6u7p7evv6BwaHhkdGK2PjW7kqNBcNrmKldyKWi1imomGkicVOpgVLolhsR8crNr59InQuVbppzjKxl7BWKo8kZ4aog8ps80RwXy81E2baUeRvNGOVtrRstQ3TWp36H4H9uYNKNagFbvk/QViCKsq1piqPaOIQChwFEgikMIRjMOT07CJEgIy4PZwTpwlJFxe4wABpC8oSlMGIPaZvi3a7JZvS3nrmTs3plJheTUof06RRlKcJ29N8Fy+cs2V/8z53nvZuZ/SPSq+EWIM2sX/p3jP/q7O1GBxh0dUgqabMMbY6XroUriv25v6nqgw5ZMRZfEhxTZg75XuffafJXe22t8zFn12mZe2el7kFXuwtacDh93H+BFtztTCohevz1fpyOeo+TGIKMzTPBdSxijU0yPsSd7jHg6e9K+/au3lL9TpKzQS+LO/2FSsroL0=</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit>: R ! R
2x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit>7 ! f (x)
t 7 ! ~ r(t) = (f (t), g (t))
Aujourd’hui nous allons explorer les fonctions vectorielles.
=
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
~ r
<latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit>: R ! R
2x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit>7 ! f (x)
t 7 ! ~ r(t)
<latexit sha1_base64="DtbUPBUzViBqsXWyjQer/0c00Go=">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</latexit><latexit sha1_base64="DtbUPBUzViBqsXWyjQer/0c00Go=">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</latexit><latexit sha1_base64="DtbUPBUzViBqsXWyjQer/0c00Go=">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</latexit><latexit sha1_base64="DtbUPBUzViBqsXWyjQer/0c00Go=">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</latexit>
= (f (t), g (t))
<latexit sha1_base64="xKgmC1tlhc4RVD8JkNQi9gmDBYE=">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</latexit><latexit sha1_base64="xKgmC1tlhc4RVD8JkNQi9gmDBYE=">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</latexit><latexit sha1_base64="xKgmC1tlhc4RVD8JkNQi9gmDBYE=">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</latexit><latexit sha1_base64="xKgmC1tlhc4RVD8JkNQi9gmDBYE=">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</latexit>~ r
<latexit sha1_base64="vk9wPTpdX5qULjbANdYSwf3Rf3k=">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</latexit><latexit sha1_base64="vk9wPTpdX5qULjbANdYSwf3Rf3k=">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</latexit><latexit sha1_base64="vk9wPTpdX5qULjbANdYSwf3Rf3k=">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</latexit><latexit sha1_base64="vk9wPTpdX5qULjbANdYSwf3Rf3k=">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</latexit>: R ! R
3= (f (t), g (t), h(t)) t 7 ! ~ r (t)
Aujourd’hui nous allons explorer les fonctions vectorielles.
=
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>y
On a déjà vu les fonctions de la forme f
<latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">AAAC6XicjVHLSsNAFD2N73fVpZtgFVyVRATFlejGpYqtQisyidN2aJIJk4ki4g+4cydu/QG3+iPiH+hfeGeMohbRCUnOnHvPmbn3BmkkMu15zyWnr39gcGh4ZHRsfGJyqjw9U89krkJeC2Uk1WHAMh6JhNe00BE/TBVncRDxg6C7ZeIHp1xlQib7+jzlRzFrJ6IlQqaJOi4vtNabMdOdIHD3mpFM2kq0O5opJc/cz8BxueJVPbvcXuAXoIJi7cjyE5o4gUSIHDE4EmjCERgyehrw4SEl7ggXxClCwsY5LjFK2pyyOGUwYrv0bdOuUbAJ7Y1nZtUhnRLRq0jpYpE0kvIUYXOaa+O5dTbsb94X1tPc7Zz+QeEVE6vRIfYv3Ufmf3WmFo0W1mwNgmpKLWOqCwuX3HbF3Nz9UpUmh5Q4g08orgiHVvnRZ9dqMlu76S2z8RebaVizD4vcHK/mljRg/+c4e0F9uep7VX93pbKxWYx6GHOYxxLNcxUb2MYOauR9hXs84NHpOtfOjXP7nuqUCs0svi3n7g0whp4h</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit><latexit sha1_base64="ytxHWl3J3El/KiKavPgwu71Bzxs=">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</latexit>: R ! R
~ r
<latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">AAAC8HicjVHLSsQwFD3W93vUpZviIAjC0IqguBp041LFUcFRSWOcCbZNSVNFxI9w507c+gNu9SvEP9C/8CZW8YFoStuTc+85yb03ymKZmyB46vA6u7p7evv6BwaHhkdGK2PjW7kqNBcNrmKldyKWi1imomGkicVOpgVLolhsR8crNr59InQuVbppzjKxl7BWKo8kZ4aog8ps80RwXy81E2baUeRvNGOVtrRstQ3TWp36H4H9uYNKNagFbvk/QViCKsq1piqPaOIQChwFEgikMIRjMOT07CJEgIy4PZwTpwlJFxe4wABpC8oSlMGIPaZvi3a7JZvS3nrmTs3plJheTUof06RRlKcJ29N8Fy+cs2V/8z53nvZuZ/SPSq+EWIM2sX/p3jP/q7O1GBxh0dUgqabMMbY6XroUriv25v6nqgw5ZMRZfEhxTZg75XuffafJXe22t8zFn12mZe2el7kFXuwtacDh93H+BFtztTCohevz1fpyOeo+TGIKMzTPBdSxijU0yPsSd7jHg6e9K+/au3lL9TpKzQS+LO/2FSsroL0=</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit><latexit sha1_base64="oR7WNJ5BDcbw+7EE5fbfezzKsyA=">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</latexit>: R ! R
2x
<latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit><latexit sha1_base64="RImMqKPne7idc0aUvLEVQmpY+54=">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</latexit>7 ! f (x)
t 7 ! ~ r(t)
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= (f (t), g (t))
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