Question

1.

(1 point)

Calculate κ(t)κ(t) when

r(t)=〈3t^(−1),5,1t〉

κ(t)=

2.

(1 point)

Find the arclength of the curve r(t)=〈−3sint,6t,−3cost〉, −9≤t≤9

Answer #1

Find the unit tangent vector T(t) and the curvature κ(t) for the
curve r(t) = <6t^3 , t, −3t^2 >.

Find the curvature of r(t) at the
point (3, 1, 1).
r(t) = <3t, t^2 , t^3>
k=

17.)Find the curvature of r(t) at the
point (1, 0, 0).
r(t) =
et
cos(t),
et
sin(t), 3t
κ =

1.
(1 point) For the curve given by
r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉,
Find the derivative
r′(t)=〈r′(t)=〈, , , 〉
Find the second derivative
r″(t)=〈r″(t)=〈
Find the curvature at t=1t=1
κ(1)=κ(1)=
2.
(1 point) Find the distance from the point (-1, -5, 3) to the
plane −4x+4y+0z=−3.

1) Find the curvature of the curve r(t)= 〈4+3t,5−5t,4+5t〉 the
point t=5.
2) Find a plane through the points (2,-3,8), (-3,-3,-6),
(-6,3,-7)

Find the curvature κ(t)κ(t) of the curve
r(t)=(−5sint)i+(−5sint)j+(−4cost)k

Find T, N, and κ for the plane curve r(t) = (7t+2) i + (5 - t^7)
j

Determine the length of the curve r(t) = 4i + 2t^2 j + 1/3t^3 k
from the point
(4, 0, 0) to the point (4, 18, 9)

1.
(1 point)
Find the distance the point P(1, -6, 7), is to the plane through
the three points
Q(-1, -1, 5), R(-5, 2, 6), and S(3, -4, 8).
2.
(1 point) For the curve given by
r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉,
Find the derivative
r′(t)=〈r′(t)=〈 , , 〉〉
Find the second derivative
r″(t)=〈r″(t)=〈 , , 〉〉
Find the curvature at t=1t=1
κ(1)=κ(1)=

6. Given vector function r(t) = t2 − 2t, 1 + 3t, 1 3 t 3 + 1 2 t
2 i (a) Find r 0 (t) (b) Find the unit tangent vector to the space
curve of r(t) at t = 3. (c) Find the vector equation of the tangent
line to the curve at t = 3

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