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Catégorie :Category: nCreator TI-Nspire
Auteur Author: knighty33
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.03 Ko KB
Mis en ligne Uploaded: 21/07/2025 - 10:50:59
Uploadeur Uploader: knighty33 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4802980
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.03 Ko KB
Mis en ligne Uploaded: 21/07/2025 - 10:50:59
Uploadeur Uploader: knighty33 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4802980
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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Identifica F × ( x , y ) vec{F}(x, y) F ( x , y ) o F × ( x , y , z ) vec{F}(x, y, z) F ( x , y , z ) Parametriza la curva: r × ( t ) vec{r}(t) r ( t ) Deriva: r × 2 ( t ) vec{r}'(t) r 2 ( t ) Evalúa F × ( r × ( t ) ) vec{F}(vec{r}(t)) F ( r ( t )) Calcula el producto punto Integra entre los valores de t t t Ejemplo (Sección 5.1): F × = ( y , 2 x ) vec{F} = (y, 2x) F = ( y , 2 x ) r × ( t ) = ( t , t 2 ) vec{r}(t) = (t, t^2) r ( t ) = ( t , t 2 ) r × 2 ( t ) = ( 1 , 2 t ) vec{r}'(t) = (1, 2t) r 2 ( t ) = ( 1 , 2 t ) F × ( r × ( t ) ) = ( t 2 , 2 t ) vec{F}(vec{r}(t)) = (t^2, 2t) F ( r ( t )) = ( t 2 , 2 t ) Producto punto: t 2 + 4 t 2 = 5 t 2 t^2 + 4t^2 = 5t^2 t 2 + 4 t 2 = 5 t 2 W = + 0 1 5 t 2 d t = 5 3 W = int_0^1 5t^2 , dt = frac{5}{3} W =0,1 + 5 t^ 2 d t = 3/ 5 F × = ( y , z , x ) vec{F} = (y, z, x) F = ( y , z , x ) r × ( t ) = ( cos a t , sin a t , t ) vec{r}(t) = (cos t, sin t, t) r ( t ) = ( cos t , sin t , t ) r × 2 ( t ) = ( sin a t , cos a t , 1 ) vec{r}'(t) = (-sin t, cos t, 1) r 2 ( t ) = ( sin t , cos t , 1 ) F × ( r × ( t ) ) = ( sin a t , t , cos a t ) vec{F}(vec{r}(t)) = (sin t, t, cos t) F ( r ( t )) = ( sin t , t , cos t ) Producto punto: sin a 2 t + t cos a t + cos a t = sin a 2 t + cos a t ( t + 1 ) -sin^2 t + t cos t + cos t = -sin^2 t + cos t(t + 1) sin 2 t + t cos t + cos t = sin 2 t + cos t ( t + 1 ) W = + 0 À sin a 2 t + cos a t ( t + 1 ) d t = À 2 2 W = int_0^pi -sin^2 t + cos t(t + 1) , dt = -frac{pi}{2} - 2 W = + 0 À sin 2 t + cos t ( t + 1 ) d t = 2 À 2 Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
Identifica F × ( x , y ) vec{F}(x, y) F ( x , y ) o F × ( x , y , z ) vec{F}(x, y, z) F ( x , y , z ) Parametriza la curva: r × ( t ) vec{r}(t) r ( t ) Deriva: r × 2 ( t ) vec{r}'(t) r 2 ( t ) Evalúa F × ( r × ( t ) ) vec{F}(vec{r}(t)) F ( r ( t )) Calcula el producto punto Integra entre los valores de t t t Ejemplo (Sección 5.1): F × = ( y , 2 x ) vec{F} = (y, 2x) F = ( y , 2 x ) r × ( t ) = ( t , t 2 ) vec{r}(t) = (t, t^2) r ( t ) = ( t , t 2 ) r × 2 ( t ) = ( 1 , 2 t ) vec{r}'(t) = (1, 2t) r 2 ( t ) = ( 1 , 2 t ) F × ( r × ( t ) ) = ( t 2 , 2 t ) vec{F}(vec{r}(t)) = (t^2, 2t) F ( r ( t )) = ( t 2 , 2 t ) Producto punto: t 2 + 4 t 2 = 5 t 2 t^2 + 4t^2 = 5t^2 t 2 + 4 t 2 = 5 t 2 W = + 0 1 5 t 2 d t = 5 3 W = int_0^1 5t^2 , dt = frac{5}{3} W =0,1 + 5 t^ 2 d t = 3/ 5 F × = ( y , z , x ) vec{F} = (y, z, x) F = ( y , z , x ) r × ( t ) = ( cos a t , sin a t , t ) vec{r}(t) = (cos t, sin t, t) r ( t ) = ( cos t , sin t , t ) r × 2 ( t ) = ( sin a t , cos a t , 1 ) vec{r}'(t) = (-sin t, cos t, 1) r 2 ( t ) = ( sin t , cos t , 1 ) F × ( r × ( t ) ) = ( sin a t , t , cos a t ) vec{F}(vec{r}(t)) = (sin t, t, cos t) F ( r ( t )) = ( sin t , t , cos t ) Producto punto: sin a 2 t + t cos a t + cos a t = sin a 2 t + cos a t ( t + 1 ) -sin^2 t + t cos t + cos t = -sin^2 t + cos t(t + 1) sin 2 t + t cos t + cos t = sin 2 t + cos t ( t + 1 ) W = + 0 À sin a 2 t + cos a t ( t + 1 ) d t = À 2 2 W = int_0^pi -sin^2 t + cos t(t + 1) , dt = -frac{pi}{2} - 2 W = + 0 À sin 2 t + cos t ( t + 1 ) d t = 2 À 2 Made with nCreator - tiplanet.org
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