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18.- Examen Parcial Calculo II 2014-II Resuelto
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Balotario Final 2016 - II
Problemas de Laplace 2016-i
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UNIVERSIDAD NACIONAL MAYOR DE SAN MARCOS (Universidad del Perú, DECANA DE AMÈRICA) FACULTAD DE INGENIERÍA ELECTRÓNICA Y ELÉCTRICA CALCULO DIFERENCIAL E INTEGRAL II EXAMEN PARCIAL 2014-II Profesor: JARA JARA NOLAN
Instrucciones: Los exámenes que utilizan lápiz y/o liquid paper no tienen derecho a reclamo. 1)
Sea la función vectorial
g ( s ) arctgs , s arctgs ,
1
2 Obtener para cualquier valor de s.
ln( s 2 1)
T (s); N (s), B(s),k (s), ( s s) y (s) Solución.
g ( s ) arctgs , s arctgs ,
1
ln( s 2 1)
2 2 1 1 2 s 1 s 2 s g ( s ) , 1 , , , 2 2 2 1 s2 1 s2 1 s2 1 s 1 s s 1 2 1 s 2 s g ( s ) 1 T ( s ) g ( s ) , , 1 s2 1 s2 1 s2
2 s 2s 2 (1 s 2 ) g ( s ) (1 s 2 ) 2 , (1 s 2 ) 2 , (1 s 2 ) 2 ; k // N Master your semester with Scribd Free Foron 30this Days Sign up to vote title 2 s Read 2 2 s 1 s 2 useful & The New ( s ) k ( sYork ) g Times ; N ( s ) , Useful , Not 2 2 2Cancel anytime. 2 Special offer for students: Only $4.99/month.1 s 1 s 1 s 1 s 2
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18.- Examen Parcial Calculo II 2014-II Resuelto
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18.- Examen Parcial Calculo II 2014-II Resuelto INFORME 7 FSK
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Balotario Final 2016 - II
Problemas de Laplace 2016-i
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Para la fu ncion vect orial f (t) ( 3t cos t,3tsent,4t)
2)
Donde t representa el tiempo y f (t) la posición de una partícula, obtener: a) la velocidad, rapidez y aceleración en cualquier instante. b) El vector tangente unitario. c) La curvatura de la curva en función del tiempo. d) Las componentes tangencial y normal de la aceleración. Solución.
f (t) ( 3 cost 3tsent,3sent 3t cost,4 )
f (t) ( 6sent 3t cost,6 cost 3tsent,0 )
a)v (t ) ( 3 cost 3tsent,3sent 3t cost,4 ) v(t ) 25 9t
2
a(t ) ( 6sent 3t cost,6 cost 3tsent,0 )
b)T (t )
( 3 cost 3tsent,3sent 3t cost,4 )
25 You're 9t 2 Reading a Preview
Unlock full access with a free trial.
c) f (t)x f (t) ( 24 cost 12tsent, 24sent 12t cost,18 9t )
2
Free f (t)x f (t) 3( 8 cost 4Download tsent, 8With sent 4Trial t cost,6 3t 2 )
f (t)x f (t) 3 100 25t k (t ) 2
15 4 t 2 (25 9t ) 2
3
2
d )aT semester a(t )T (t ) with Scribd Master your Read Free Foron 30this Days Sign up to vote title ( 3 cost 3Useful tsent,3sent 3t cost,4 ) & The New York Times Not useful ( 6sent 3t cost,6 cost 3tsent,0 ).
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25 9t
2
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18.- Examen Parcial Calculo II 2014-II Resuelto
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Balotario Final 2016 - II
Problemas de Laplace 2016-i
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Representemos la trayectoria por la función vectorial
f (t) (x (t ), y (t ) ) Un vector tangente a la trayectoria será:
f (t) ( x(t ), y(t ) ) Como el rastreador busca el máximo incremento de temperatura, entonces
f (t) // T ( x, y ) T ( x, y ) k f (t) x(t ) 8 x k 8 x,2 y k x(t ), k y(t ) y (t ) 2 y k
dx
( x, y ) (2,3) c
81
y ( x )
y
4 x
4
dy y
x
2
4 ln y ln(cx) y 4 cx x
2
y 81
4
You're Reading a Preview
4) Dada la función f (x,y) = 9x²- 2xy + 4y², determine los valores extremos absolutos de f Unlock fulllaaccess with a free trial.= 36 sobre la región del plano encerrado por elipse 9x² + 4y² Solución. f x 18 x 2 y 0 y 9 x f y 2 x 8 y 0 y
x
4
Download With Free Trial
( x, y ) (0,0) f (0,0) 0
x 2 cos t f (t ) 36 12sent cos t 36 6sen(2t ) f (t ) 12 cos(2t ) y 3 sent
Master your semester with Scribd Foron 30this Days Sign to vote title 3 5 3 Read 5 upFree f (t ) 0 2t , , , t , , , & The New York Times 2 2 2 4 4 4Useful Not useful
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f ( ) 30; f ( ) 42; 4 4
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