Question

What is the equation of the osculating plane of the curve X(t) = (sin t, cost, t) at t =π

Answer #1

Find equations of the normal plane and osculating plane of the
curve at the given point
x = sin(2t), y = t, z = cos(2t)
at (0, pi, 1)

Consider the parametric curve C deﬁned by the parametric
equations x = 3cos(t)sin(t) and y = 3sin(t). Find the expression
which represents the tangent of line C. Write the equation of the
line that is tangent to C at t = π/ 3.

Find the osculating plane of r(t) =< t2, 32 t3, t > at (1,
2/3, 1)

7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3
sin(t), t ∈ [0, 2π) Part a: (2 points) Give an equation relating x
and y that represents the curve. Part b: (4 points) Find the slope
of the tangent line to the curve when t = π 6 . Part c: (4 points)
State the points (x, y) where the tangent line is horizontal

The continuous time signal x(t) = 2*sin
(2*π*100*t +
π/2) + sin (2*π*150*t) +
3*sin (2*π*300*t) is
sampled at 500 samples per second.
Write the mathematical expression x(n) of the sampled discrete
time signal. Show your work.
What are the discrete time frequencies obtained in
x(n)?

1.Let y=6x^2. Find a parametrization of the
osculating circle at the point x=4.
2. Find the vector OQ−→− to the center of the
osculating circle, and its radius R at the point
indicated. r⃗
(t)=<2t−sin(t),
1−cos(t)>,t=π
3. Find the unit normal vector N⃗ (t)
of r⃗ (t)=<10t^2, 2t^3>
at t=1.
4. Find the normal vector to r⃗
(t)=<3⋅t,3⋅cos(t)> at
t=π4.
5. Evaluate the curvature of r⃗
(t)=<3−12t, e^(2t−24),
24t−t2> at the point t=12.
6. Calculate the curvature function for r⃗...

For the curve x = t - sin t, y = 1 - cos t find d^2y/dx^2, and
determine where the curve is concave up and down.

Find the equation of the osculating
circle of the parabola y =
x^2 at the
origin.

In this problem, x = c1 cos t + c2 sin t is a two-parameter
family of solutions of the second-order DE x'' + x = 0. Find a
solution of the second-order IVP consisting of this differential
equation and the given initial conditions.
x(π/6) = 1 2 , x'(π/6) = 0
x=

Consider the curve r(t) = cost(t)i + sin(t)j +
(2/3)t2/3k
Find:
a. the length of the curve from t = 0 to t = 2pi.
b. the equation of the tangent line at the point t = 0.
c. the speed of the point moving along the curve at the point t
= 2pi

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