Sketch the plane curve. r(t) = 36 - ti. [0. 3] 0 Find its length over the given interval. E Sketch the space curve. Interval Function [0, 1] r(t) = -ti + 4tj + 3tk Z Z 5 15 5 5 - 2 X - 2 2 X 2 O O Z Z 5 5 - 2 X -2 2 X 2 O O Find its length over the given interval.Consider the helix represented by the vector-valued function r(t) = (2 cos(t), 2 sinCt), t). (a) Write the length of the art 5 on the helix as a function of t by evaluating the integral below. I 5 =1 [X'M]2 + [)"(UH2 + [Z'(U)]2 d\" (b) Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameters. r(s) = (c) Find the coordinates of the point on the helix For the following arc lengths. (Round your answers to three decimal places.) s=\\/5ands=4 5=\\/ (X.y,z)=( ) s=4 (X.y.2)=( ) (d) Evaluate ||r'(s)| I. llr'(S)|l =|:| Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + 2 s it 1 - 2 S 2 2 K =