Question

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)

Answer #1

Find the equation of the line tangent to the parametric curve x
= t2 − 2t3 y = t2 when t = 2.

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

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.

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

1. Graph the curve given in parametric form by x = e t sin(t)
and y = e t cos(t) on the interval 0 ≤ t ≤ π2.
2. Find the length of the curve in the previous problem.
3. In the polar curve defined by r = 1 − sin(θ) find the points
where the tangent line is vertical.

Find parametric equations for the rectangular equation y = e^x +
9 using the parameter t = dy/dx . Verify that at t = 1, the point
on the graph has a tangent line with slope 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.

On the parametric curve (x(t), y(t)) = (t − t^2 , t^2 + 3t)
pictured below, determine the (x, y)-coordinates of the marked
point where the tangent line is horizontal.

the curve shown below has parametric equations : x =
t2 - 2t +2, y = t3 - 4t (- infinity <t
< infinity).
find the value of t which gives point (10,0) on the curve, and
determine the slope of the curve at this point.

Consider the parametric curve given by the equations:
x = tsin(t) and y = t cos(t) for 0 ≤ t ≤ 1
(a) Find the slope of a tangent line to this curve when t =
1.
(b) Find the arclength of this curve

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