Consider the circular helix with equation R(t) = (12t, 5cost, (a) Find the value of t such that R(t) = (67,0, –5). (b) Reparametrize R(t) using the arclength parameter s fror
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- Compute the arc length of the parametric curve given X=1/3t^3-t,y=t^2+3 From t=0 to t=3For the curve x = sin(t) - tcos(t), y = cos(t) + tsin(t), z = t2, find the arc length between (0, 1, 0) and (-2π, 1, 4π2).Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0, 2π] .
- Find the arc length of the curve given in parametric form by c(t) = (t^3, t^2) for 0 ≤ t ≤ 1.Consider the parametric equation x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2). (b) Set up, but do not evaluate, and integral representing the arc length over the interval 2 ≤ t ≤ 4.Given R(t) = (1 – 4 cos t) î + 3 cos ĵ + 5 sin t k̂, find the arc length of the portion of R(t) from t = 0 to t = π; moving trihedral of the curve R(t) at t =π/3
- Find the arclength of the curve x= 4cos(6t), y= 4sin(6t) with 0 less than or equal to t less than or equal to pi/18Consider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)]Compute the arclength function s(t): (with initial point t=0).Find T(t) and then find a set of parametric equations for the tangent line to the helix given by r(t) = 2 cos ti + 2 sin tj + tk at the point (√2, √2, π/ 4).
- Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2). (b) Set up, but do not evaluate, an integral representing the arc length over the interval 2 ≤ t ≤ 4.Find the point on the curver(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13p units along the curve from the point (0, -12, 0) in the direction opposite to the direction of increasing arc length.a) Find the arc length parametrization of the line x = t, y = t that has the same orientation as the given line and has reference point (0, 0).(b) Find the arc length parametrization of the line x = t, y = t, z = t