Advanced Math Archive: Questions from June 10, 2023
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Considere las ciudades B,C,D,E,F,G
Los costos de las posibles carreteras entre ciudades se dan a
continuación:
c(B,F) = 11
c(B,G) = 10
c(C,G) = 8
c(D,E) = 12
c(D,F) = 13
c(E,F) = 9
c(E,G) = 7
¿Cuál
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Sea f(x,y,z)=x+yz y sea C el segmento de línea de P=(0,0,0) a
(6,9,2).
(a) Calcule f(c(t)) y ds=∥c′(t)∥dt para la parametrización
c(t)=(6t,9t,2t) para 0≤t≤1.
(b) Evalúe ∫ c f(x,y,z)ds=
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Considere el campo vectorial
F(x,y,z)=(−2y,−2x,7z)F(x,y,z)=(−2y,−2x,7z). Muestre que F es un
campo vectorial gradiente F=∇V determinando la función V que
satisface V(0,0,0)=0V(0,0,0)=0.
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¿Cuál es la distancia vertical máxima entre la parábola
~y=3-x^2~ y=3−x2 space, y, equals, 3, minus, x, squared, space y la
recta ~y=x+1~ y= x+1 space, y, equals, x, plus, 1, space for ~-2\le
x\
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