1) Obtain the arc length of the following vector function. (t) = ½t²t+ sin(t)j — cos(t) k 0sts4

Q: Find the arc length (s) of the curve 7(t) = (4 cos( – 4t), 2/5 cos( – 4t), 6 sin( – 4t)) for 0 <t <…

A: Given that  The curve is  To find the arc length of the curve

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

A:

Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

A:

Q: 3. Consider the curve 7 (t) = (1, t², *) Find the arc length from t = 0 to t = V5. Note: you might…

A: As we know that the expression of the arc length for the parametric curve is:…

Q: Find an arc length parametrization r(t) = (et sin(t), et cos(t), 7et). Assume t(s) = 0 when s = 0,…

A: Given: The given vector is rt=etsint, etcost, 7et. To find: The arc length parametrization r1s of…

Q: Find the arc length (s) of the curve r(t) = (2t, 4 cos(3t), 4 sin(3t)) for 1 <t < 4 S =

A: Application of integration and partial derivatives use to solve this problem.

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find an arc length parametrization r(t) = (e¹ sin(t), et cos(t), 7eª). Assume t(s) T1(s) = (0) =…

A: Introduction: If s=∫0sg'(t)dt, the arc length of a curve drawn by the vector-valued function g(s) is…

Q: Find the arc length of the curve c(t) = (5 cos(t), 5 sin(t), -13t) on the interval 0 ≤ t ≤ 2.…

A:

Q: Find the arc length of the parametric curve (sin² t)i + (cos²t)j, 0<t<5

A: Given parametric curve is r(t)=sin2ti+cos2tj,            0≤t≤π2 From the given curve,…

Q: Q4. Find the arclength of the curve given by the equation r(t)= (5 cos t², 5 sin t2,12 t²), for 0 ≤…

A: formula for arc lenth is  L=∫ab(dxdt)2+(dydt)2+(dzdt)2dtgiven x(t)=5cost2         y(t)=5sint2…

Q: Find the arc length of the curve c(t) = (cos(9t), sin(9t), 2t³/2) on the interval 0 ≤ t ≤ 1.…

A:

Q: Let r(t) = (2 sin (t), +2, 3cos (t)) 2π 1. Find the unit tangent vector T(t) 2. Find T'(t) 3. Find…

A:

Q: Consider the curve r = (e-¹t cos(-6t), e-¹ sin(-6t), e-¹t). Compute the arclength function s(t):…

A: Consider the curver = (e-t cos(-6t), e-t sin(-6t), e-t )We have to Compute the arclength function…

Q: 1. Given the vector-valued for R(t) = (2 sin 2t-1)i+ 2 cos 2tj+ 3tk. %3D (a) Find the length of the…

A: Given that Rt=2sin2t−1i+2cos2tj+3tk