Find the derivative, r'(t), of the vector function. r(t) = cos (at) i + tebt; + sin2(ct) k r'(t) = -asin (2at )i + e(bt + 1 )j + c sin(2ct) k XFind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. X = V t2 + 63, y = In(t2 + 63), z = t; (8, In(64), 1) (x (t ) , y (t ), z (t ) ) =Find the point on the curve r(t) = (8 cos(t), 8 sin(t), er), 0 S t 2 TI, where the tangent line is parallel to the plane \"EX + y = 1. (x,y.z)=( ) Find parametric equations For the tangent line to the curve with the given parametric equations at the specified point. x = 10 cos(t), y = 10 sin(t), z = 2 cos(2t), (S, 5, 1) W), mar =(S ) Illustrate by graphing both the curve and the tangent line on a common screen. (The tangent line will be plotted for 1 S t S 1. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) Student Response Response Update Description Graph \fEvaluate the integral. (Use C for the constant of integration.) 4 it tete j + 6\\tk dt 1+ +2 10 /05 4 tan 1 ti + 2 + 4t + C X