Compute the derivative for r(t) = (1,15,16). r(1) ) = (f(1), g(t), h(t)) dt (Use symbolic notation and fractions where needed.) f(1) = g(t) = h(t) = Find the location at t = 3 of a particle whose path satisfies 5 = - (101 - (+$12,21-4) dr dt r(0) = (6,13) (Use symbolic notation and fractions where needed. Give your answer in vector form.) r(3) = Find the solution with the given initial condition. r" (t) = (e, sin (), cos (t)), r(0) = (1,0,1), r'(0) = (0,5,5) (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) r(t) = Evaluate the integral. * (- sin (1), 61, 21 + cos (21) dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) 2x 1.2 (-sin (1), 61, 2t + cos (21)) dt = Calculate the velocity and acceleration vectors at the time t = 1. r(t) = (1,1-31, 51) (Give your answers using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) velocity: acceleration: Calculate the speed at the time t = 1. (Give an exact answer. Use symbolic notation and fractions where needed.) speed: Find r(t) and the velocity vector v(1) given the acceleration vector a(t) = (7e, 81, 20r + 8), the initial velocity v(0) = (1,0,1), and the position r(0) = (2, 1, 1). (Use symbolic notation and fractions where needed. Give your answer in the vector form.) v(t) = r(t) = Find a parametrization of the tangent line at the point indicated. r(t) = (61,41,21), 1=4 Identify the parametrization(s) of the tangent line at t = 4. (1)=(24, 64, 128) +1(6,32,96) L3 (1) = (128, 24,64)+1(9, 32,192) Ls(t) = (12,98, 195)+1(-6, -32,-96) L(t) = (36, 32, 320)+1(6,32,96) L4 (1) = (36, 128, 320)+1(12, 64, 192)