Question

Parameterize the curve using the arc-length parameter s, at the point at which t=0t=0 for r(t)=e^tsint i+e^tcost j.

Answer #1

find the length of the curve r(t)=(tsint+cost)i+(tcost-sint)j from
t=sqrt(2) to 2

Write the curve given by r(t)=((3/2)t)i+(t^3/2)j as a function
r(s) parameterized by the arc length s from the point where t=0.
Write your answer using standard unit vector notation.

Calculate the arc length of the indicated portion of the curve
r(t).
r(t) = 6√2 t^((3⁄2) )i + (9t sin t)j + (9t cos t)k ; -3 ≤ t ≤
7

For the curve x = sint - tcost, y = cost + tsint, z =
t2
find the arc length between (0, 1, 0) and (-2π, 1,
4π2)
I have gotten down to tsqrt(5) but how am I supposed to assign
the bounds given 3 variables in space and not only 2?

Find, for 0 ≤ x ≤ π, the arc-length of
the segment of the curve R(t) = ( 2cost − cos2t, 2sint −
sin2t )
corresponding to 0 ≤ t ≤ x.

. Find the arc length of the curve r(t) = <t^2 cos(t), t^2
sin(t)> from the point (0, 0) to (−π^2 , 0).

Find the arc length of the curve r(t) = i + 3t2j +
t3k on the interval [0,√45].
Hint: Use u-substitution to integrate.

Parametrize the curve r(t) = <5sin(t), 5cos(t), 12t> with
respect to arc length, measured from the point (0,5,0).

Consider the parametric curve given by x ( t ) = e t c o s ( t )
, y ( t ) = e t s i n ( t ) , t ≥ 0.
Find the arc-length of this curve over the interval 0 ≤ t ≤
3.

1. a) Get the arc length of the curve.
r(t)= (cos(t) + tsin(t), sin(t) - tcos(t), √3/2 t^2) in
the Interval 1 ≤ t ≤ 4
b) Get the curvature of r(t) = (e^2t sen(t), e^2t, e^2t cos
(t))

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