VI. Let C be a space curve defined by the vector-valued function R(t) = (sin t cost, sin² t, √3t). Let P (0,1, ³) be a point on C. 1. Reparametrize R(t) using the arc length s measured from the point P in the direction of increasing values of t. 2. Find the coordinates of the point Q located units along C from the point P.

Q: #2. Consider the following vector function. r(t) = (t,3t²,-t²). (a) Find the arc length function.…

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Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

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Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

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Q: At which point does the parametric curve given by x = 2 cost y = 2 sin t z = 2t - π/3 cross the…

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

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Q: Find the arc length function s(t) for r, (t) = (e' sin(t), e' cos(t), e) where t 2 0. Then…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

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Q: Q2) consider a particle moving in a curve defined by F(t) =sin 21, cos 21, 1. Find a. The velocity…

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Q: For the curve defined by F(t) = (e¯', 4t, e') find the unit tangent vector, unit normal vector,…

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Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(zt) î + at j+ sin(rt) k. %3D…

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Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

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Q: Use Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the…

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Q: 4. Find the unit tangent vector T(t) to the curve r(t) = (In(cos t), cost, sin t) at time t. (a)…

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Q: Let be a curve defined by the vector function (t)= 6ti + çin 2t -cos 2+ k 3- and Find the moving…

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Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (c) Determine the…

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Q: Please show full solution for thumbs up!

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