Question

Find the exact length of the curve y=(x^3)/3 + 1/(4x) for 2≤x≤3

Conslder the curve deflned by x=t+1 and y=t^2. Find the corresponding rectangular equation. Produce two graphs: one using the rectangular equation and one using the parametric equations. What are the differnce's between the graphs?

Please show work.

Answer #1

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Find the exact length of the curve.
Part A
x = 4 + 12t2, y = 7 + 8t3 , 0 ≤ t ≤ 1
Find the exact length of the curve.
Part B
x = et - 9t, y = 12et/2 , 0 ≤ t ≤ 2

Find the exact length of the curve.
x = 4 +
12t2, y
= 1 + 8t3, 0 ≤
t ≤ 3
please give answer with radicals. cannot have decimals.

Find the exact length of the curve.
x = 9 +
12t2, y
= 2 + 8t3, 0 ≤
t ≤ 5

1) Find the length of the parametric curve x=2 cos(t)
, y=2 sin(t) on the interval [0, pi].
2) A rope lying on the floor is 10 meters long and its
mass is 80 kg. How much work is required to raise one end of the
rope to a height of 15 meters?

Find parametric equations for the curve of intersection of the
cylinders x^+y^2=1 and x^2+z^2=1. Use 3D Calc Plotter to graph the
two surfaces. Then graph your parametric equations for the curve of
intersection. Use a different constant primary color for each of
your parametric curves. Print out your graph.
I need help on how to do this using 3D Calc Plotter please.
Thank you.

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.

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

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

1) Sketch the graph?=? ,?=? +3,and include orientation.
2) Sketch the graph ? = sin ? , ? = sin2 ? + 3 and include
orientation.
3) Remove the parameter for ? = ? − 3, ? = ?2 + 3? − 2 and write
the corresponding
rectangular equation.
4) Remove the parameter for ? = 2 + 3 sin ? , ? = −1 + 3 cos ?
and write the corresponding rectangular equation.
5) Create a parameterization for...

Find the arc length of the curve on the given interval. (Round
your answer to three decimal places.)
Parametric Equations
Interval
x = 6t + 5, y = 7 − 5t
−1 ≤ t ≤ 3

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