r(t)=[cos(t),sin(t),cos(3t)]
r(t)=[tcos(t),tsin(t),t)
r(t)=[cos(t),sin(t),t2]
r(t)=[t2cos(t),t2sin(t),t]
r(t)=[cos(t),t,sin(t)]
Sketch the graphs.
r(t)=[cos(t),sin(t),cos(3t)]
r(t)=[tcos(t),tsin(t),t)
r(t)=[cos(t),sin(t),t2]
r(t)=[t2cos(t),t2sin(t),t]
r(t)=[cos(t),t,sin(t)]
Sketch the graphs.
Consider the following vector function.
r(t) =
6t2, sin(t) − t cos(t), cos(t) + t sin(t)...
Consider the following vector function.
r(t) =
6t2, sin(t) − t cos(t), cos(t) + t sin(t)
, t > 0
(a) Find the unit tangent and unit normal vectors
T(t) and
N(t).
T(t)
=
N(t)
=
(b) Use this formula to find the curvature.
κ(t) =
Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉r1=〈sin(t),t,t^2〉 and
r2=〈cos(t),1−t,t^3〉.r2=〈cos(t),1−t,t^3〉. If the temperature for...
Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉r1=〈sin(t),t,t^2〉 and
r2=〈cos(t),1−t,t^3〉.r2=〈cos(t),1−t,t^3〉. If the temperature for
the points is given by T(x,y,z)=x^2y(5−z),T(x,y,z)=x^2y(5−z), use
the Chain Rule to determine the rate of change of the difference D
in the temperatures the two spacecraft experience at time t=2.
(Use decimal notation. Give your answer to two decimal
places.)
Let c(t) = (t^2, t sin(π t), t cos(π t)). Find the intersection
point of the...
Let c(t) = (t^2, t sin(π t), t cos(π t)). Find the intersection
point of the tangent line to c at t = 3 with the yz-plane?