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. 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...

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 length of the curve defined by the parametric
equations
x=(3/4)t y=3ln((t/4)2−1)
from t=5 to t=7.

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.
y2 = 4(x + 3)3, 0 ≤ x ≤
1, y > 0

Calc 2: Please make sure these are right!!
Find the exact length of the curve.
x = 8 + 9t^2 ,
y = 4 + 6t^3,
0 ≤ t ≤ 3

find the exact length of the curve( y=1 - 1/e^x) ,
0<x<2.
Thanks!

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

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.

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?

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