Consider the helix
r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t).
Compute, at t=π/6
A. The unit tangent vector T=T= ( , , )
B. The unit normal vector N=N= ( , , )
C. The unit binormal vector B=B= ( , , )
D. The curvature κ=κ=
If u(t) = < sin(8t), cos(4t), t > and v(t) = < t,
cos(4t), sin(8t) >, use the formula below to find the given
derivative.
d/(dt)[u(t)* v(t)] =
u'(t)* v(t) +
u(t)* v'(t)
d/(dt)[u(t) x v(t)] =
<.______ , _________ , _______>
If u(t) = < sin(5t),
cos(5t), t > and
v(t) = < t, cos(5t),
sin(5t) >, use the formula below to find the given
derivative.
d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t)
d/dt [ u(t) x v(t)] = ?
a) Calculate and plot the DTFT of ?[?] = sin( (?/ 4)?) / ?? *
cos ( ?/2 ?) by hand.
b) By using a 2x1 subplot, plot ?[?] signal defined in Question
1 in the first row. Take ? between -100 s and 100 s and limit
x-axis between -20 sand 20 s. Be careful about when ? = 0. What is
the value of ?[0]? While plotting ?[?] please write an if statement
for ? = 0. After...
The plane curve represented by x(t) = t − sin(t), y(t) = 7 −
cos(t), is a cycloid.
(a) Find the slope of the tangent line to the cycloid for 0 <
t < 2π.
dy
dx
(b) Find an equation of the tangent line to the cycloid at t
=
π
3
(c) Find the length of the cycloid from t = 0 to t =
π
2
The cycloid has parametric equations x = a(t + sin t), y = a(1 -
cos t). Find
the length of the arc from t = 0 to t = pi. [ Hint: 1 + cosA = 2
cos2 A/2 ]. and the arc length of a
parametric