Find all horizontal and vertical tangent lines for the
parametric curve defined by x(t) = t^3...
Find all horizontal and vertical tangent lines for the
parametric curve defined by x(t) = t^3 - 3t +1, y(t) = 4t^2 +5.
then write our the equations for the tangent lines
Solve the problem
43) Find equations for the horizontal and vertical tangent lines
to the curve r = 1 - sinθ, 0 ≤ θ < 2π.
Please check if your answer is correct with the following:
Horizontal: y = 1/4 at (1/2, π/6), y = 1/4 at (1/2, 5π/6), y =
-2 at (2, 3π/2)
Vertical: x = 0 at (0, π/2), x = -3sqrt(3)/4 at (3/2, 7π/6), x =
3sqrt(3)/4 at (3/2, 11π/6)
A curve c is defined by the parametric equations
x= t^2 y= t^3-4t
a) The curve C has 2 tangent lines at the point (6,0). Find
their equations.
b) Find the points on C where the tangent line is vertical and
where it is horizontal.
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.)
z = x2 +
y2, z = 16 −
y, (4, −1, 17)
Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at the given point. (Enter
your answers as a comma-separated list of equations.) z = sqrt(x2 +
y2) , 9x − 3y + 5z = 40, (3, 4, 5)
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$
Find the point of intersection of the tangent lines to the curve
r(t) = 5 sin(πt), 2 sin(πt), 6 cos(πt) at the points where t = 0
and t = 0.5. (x, y, z) =
Find an equation of the tangent to the curve x = 2 + ln t, y =
t2 + 4 at the point (2, 5) by two methods.
(a) without eliminating the parameter
(b) by first eliminating the parameter
Find the distance between the skew lines with parametric
equations x = 1 + t, y = 3 +
6t, z = 2t, and
x = 1 + 2s, y = 6 + 15s, z
= −2 + 6s.
Find the equation of the line that passes through the points on
the two lines where the shortest distance is measured.