contestada

Show that the given curve c(t) is a flow line of the given velocity vector field F(x, y, z).

c(t) = (2 sin(t), 2 cos(t), 9et); F(x, y, z) = (y, −x, z)

c'(t) = ?

F(c(t)) = ?

Respuesta :

Answer:

a) [tex]c'(t) = (2 Cos(t), -2 Sin(t), 9e^t) [/tex]

b) [tex]c'(t) = (2 Cos(t), -2 Sin(t), 9e^t) [/tex]

Step-by-step explanation:

We are given in the question:

[tex]c(t) = (2 Sin(t), 2 Cos(t), 9e^t)[/tex]

F(x,y,z) = (y, -x, z)  

a) [tex]c'(t) [/tex]

We differentiate with respect to t.

[tex]c'(t) = (2 Cos(t), -2 Sin(t), 9e^t) [/tex]

b) F(c(t))

This is a composite function.

[tex]F(c(t)) = F(2 Sin(t), 2 Cos(t), 9e^t)[/tex]

[tex]= (2 Cos(t), -2 Sin(t), 9e^t)[/tex]

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