Question

Find parametric equations for the tangent line to the curve r(t)= <t^7, t^6, t^5> when t=1

Answer #1

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point. x = 6
cos(t), y = 6 sin(t), z = 10 cos(2t); (3 3 , 3, 5)
x(t), y(t), z(t) = ??

Find T(t) and find a set of parametric equations for the line
tangent to the space curve at the point P0, which
corresponds to t0 = 1
r(t) = ln ti + (1/t) j +9tk

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−5t
cos(5t), y =
e−5t
sin(5t), z =
e−5t; (1, 0, 1)

Find parametric equations for the tangent line to the curve with
the given parametric equations at the specified point.
x =
e−8t
cos(8t), y =
e−8t
sin(8t), z =
e−8t; (1, 0, 1)

Find the slope of the tangent line to the parametric curve
indicated by the equations below:
LaTeX: = square root t 2 + 2 t
LaTeX: x= 2/5 e t + t
LaTeX: t = 2 Round your answer to 2 decimal places.

Find the parametric equations for the tangent line to the curve
that is the intersection of the paraboloid z=4x^2+y^2 and the
parabolic cylinder y=x^2 at the point (1,1,5).

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

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 = 9 −
y, (3, −1, 10)

Find a set of parametric equations for the tangent line to the
curve of intersection of the surfaces at given point
z=x^2+y^2,z=16-y,(4,-1,17)

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

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