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- Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by the vector fieldF(x, y) = <x^(3)−2y^(2), x + cos(√y)> on a particle moving along C.Suppose that r(u)r(u) is a vector valued function of uu, and suppose dr/du(3)=(0.5933,−0.3068,0.4641).drdu(3)=(0.5933,−0.3068,0.4641). A particle moves in three dimensional space along the reparametrized curve r(u), where u=2t+t^3. What is the speed of the particle at time t=1?
- Der. 3D 19 0 Find the unit tangent vector at the point with the givenvalue of the parameter t.give the position vectors of particles moving alongvarious curves in the xy-plane. In each case, find the particle’s velocityand acceleration vectors at the stated times, and sketch them asvectors on the curve. Motion on the parabola y = x2 + 1r(t) = ti + (t2 + 1)j; t = -1, 0, and 1Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P (1, 1), in which z = 1. The value of the directional derivative of z at P in the direction of the vector w = (1, −1), corresponds to:
- Suppose a > 0the vector function that describes the motion of a particle for t ≥ 0. Find the tangential and normal components of accelerationIn Exercises 1–8, find the curve’s unit tangent vector. Also, find thelength of the indicated portion of the curve. PROBLEM 8 PLEASE. 8. r(t) = (t sin t + cos t)i + (t cos t - sin t)j,Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to: