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1. [-/1 Points] DETAILS LARCALC11 12.4.007. MY NOTE Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4ti - In(t)j, t = e T(e) = Need Help? Read It Watch It 2. [-/1 Points] DETAILS LARCALC11 12.4.013.MI. MY NOTE Find the unit tangent vector T(t). r(t) = (5 cost, 5 sin t, 2), P( V z, 2) Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization. Need Help? Read It Watch It Master It 3. [-/1 Points] DETAILS LARCALC11 12.4.018. Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) = v2ti + elj + elk, t =04. [-/1 Points] DETAILS LARCALC11 12.4.023. MY NOTES Sketch the graph of the plane curve r(t) and the vectors T(t) and N(t) at the given value of t. r(t) = (2t+ 1)i tz', t = 2 5. [-/1 Points] DETAILS LARCALC11 12.4.029. Find the tangential and normal components of acceleration at the given time t for the plane curve r(t). r(t) = e cos(t)i + e sin(t)j, t = It 2 aT an = Need Help? Read It Watch It 6. [-/1 Points] DETAILS LARCALC11 12.4.039. Find the tangential and normal components of acceleration at the given time t for the space curve r(t). (If an answer is undefined, enter UNDEFINED.) r(t) = e sin(t)i + e cos(t)j + elk, t = 0 aT aN7. [-/1 Points] DETAILS LARCALC11 12.4.045. The figure shows the path of a particle modeled by the vector-valued function below. r(t) = (nt - sin(nt), 1 - cos(nt)) The figure also shows the vectors v(t)/| |v(t) | | and a(t)/| |a(t) | | at the indicated values of t. 1= 2 1 = 1 (a) Find aT and a at t = L, t = 1, and t = N / W t = t = 1 t = N W aT aN (b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. 1 :po. . ..... t = ---Select--- v t = 1 ---Select--- t = N W ---Select