Question

Find the equation of the line tangent to the parametric curve x
= t^{2} − 2t^{3} y = t^{2} when t = 2.

Answer #1

two part question:
a) graph the parametric equation x=t2-t , y=t2+t+1 only on the
interval -1<t<2
b) find an equation of the tangent line to the curve at the
point (0,3)

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) = ??

Consider the parametric curve
x = t2, y = t3 + 3t, −∞ < t < ∞.
(a) Find all of the points where the tangent line is
vertical.
(b) Find d2y/dx2 at the point (1, 4).
(c) Set up an integral for the area under the curve from t = −2
to t = −1.
(d) Set up an integral for the length of the curve from t=−1 to
t=1.

a) Find the equation of the tangent line to the curve x= 2sin2t,
y= 3sint at the point where the same.
b) Find the points on the curve x= t^2-t+2, y=t^3-3t where the
tangent is horizontal.

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 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 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 equation of a tangent line to the curve x = ( square
root of t) / (1+t^2) at t = 4

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.

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