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# razon de cambio

Module by: diego diaz torres. E-mail the author

Summary: razon de cambio 2

Razon de Cambio

si el Volumen de un cilindro aumenta a razon de 3 cm 3 / seg . Calcular la razon de cambio de la superficie del cilindro en elinstante cuando h = 1 y sabiendo que h = 3 r . si el Volumen de un cilindro aumenta a razon de 3 cm 3 / seg . Calcular la razon de cambio de la superficie del cilindro en elinstante cuando h = 1 y sabiendo que h = 3 r .
(1)
DESARROLLO DESARROLLO
(2)
V C = 3 π r 3 V C = 3 π r 3
(3)
dV dt = 9 π r 2 dr dt dV dt = 9 π r 2 dr dt
(4)
3 = 9 π r 2 dr dt 3 = 9 π r 2 dr dt
(5)
dr dt = 1 3 π r 2 cm / seg dr dt = 1 3 π r 2 cm / seg
(6)
S = 6 π r 2 + 2 π r 2 S = 8 π r 2 S = 6 π r 2 + 2 π r 2 S = 8 π r 2
(7)
dS dt = 16 π r dr dt dS dt = 16 π r 1 3 π r 2 dS dt = 16 π r dr dt dS dt = 16 π r 1 3 π r 2
(8)
dS dt = 16 3 r cm 2 / seg dS dt = 16 3 r cm 2 / seg
(9)
si h = 1 r = 1 3 dS dt = 16 cm 2 / seg si h = 1 r = 1 3 dS dt = 16 cm 2 / seg
(10)

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