Question

Find the length of the curve x= (3t - t)^3, y = 3(t^2) for 0 ≤ t ≤ 2

Answer #1

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Find the length of the curve x = 3t^(2), y = 2t^(3) , 0 ≤ t ≤
1

Find the curvature of the space curve x=(3t^2)-t^3 y=3t^2
z=(3t)+t^3

Find the length of the curve.
x=11t^3 , y=(33/2)t^2, 0 less than or equal to t less than or
equal to sqrt. 3
The length of the curve at x==11t^3, y=(33/2)t^2, 0 less than or
equal to t less than or equal to sqrt. 3 is _____

Consider the parametric curve defined by x = 3t − t^3 , y = 3t^2
. (a) Find dy/dx in terms of t.
(b) Write the equations of the horizontal tangent lines to the
curve
(c) Write the equations of the vertical tangent lines to the
curve.
(d) Using the results in (a), (b) and (c), sketch the curve for
−2 ≤ t ≤ 2.

Find the derivative of the parametric curve x=2t-3t2,
y=cos(3t) for 0 ≤ ? ≤ 2?.
Find the values for t where the tangent lines are horizontal on
the parametric curve. For the horizontal tangent lines, you do not
need to find the (x,y) pairs for these values of t.
Find the values for t where the tangent lines are vertical on
the parametric curve. For these values of t find the coordinates of
the points on the parametric curve.

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0
≤ t ≤ 5
Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =
Find dy/dx. x = t 3 + t , y = 3 + t
Find the distance traveled by a particle...

At what point on the curve
x = 3t^2 + 1, y = t^3 − 3 does the tangent line have slope 1/2
?

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

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.

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.

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