The space curve 7(t) = (t, t, t) is known as the twisted cubic and it is shown below: Match each coordinate plane with the projection of the twisted cubic into that plane. |cz-plane ] yz-plane | xy-plane a. -5 -4 -3 -2 -2 -3 -4 -5+ 4 Б. -5 -4 -3 -2 -- -2

Do c

Let f(x, y) = xy² and r(t) = (¹/1²,t³). Calculate Vf. (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) Vf= Calculate r' (t). (Use symbolic notation and fractions where needed. Express numbers in exact form. Give your answer in the form (*, *). ) r' (t) = Use the Chain Rule for Paths to evaluateƒ(r(t)) at t = 1.5. (Use decimal notation. Give your answer to three decimal places.) d dt - ƒ(r(1.5)) = = Use the Chain Rule for Paths to evaluate ƒ(r(t)) at t = -1.7. (Use decimal notation. Give your answer to three decimal places.) d dt d f(r(-1.7)) =