Question

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) = ??

Answer #1

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)

Determine the tangent line at point t = π/3 of the curve defined
by the parametric equations:
X = 2 sin (t)
Y = 5 cos (t)

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)

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 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).

find an equation for the line tangent to the given curve at the
point defined by the given value of t.
x sin t + 2x =t, t sin t - 2t =y, t=pi

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)

Given parametric equations below, find d^2y/dx^2 and determine
the intervals on which the graph of the curve is concave up or
concave down.
(a) x = t^2 , y = t^3−3t
(b) x = cos(t), y = sin(2t)

Find parametric equations of the line that passes through (1, 2,
3) and is parallel to the plane
2 x − y + z = 3 and is perpendicular to the line with parametric
equations:
x=5-t, y=3+2t , z=4-t

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