Given the force field F, find the work required to move an object on the given orientated curve. F = (y,x) on the parabola y = 7x² from (0,0) to (3,63) The amount of work required is (Simplify your answer.)

2) Consider a bicyclist whose position s(t), in feet, is given by the table where t is in seconds. t 6 7 8 9 10 11 s(t) 60 90 110 119 124 128 130 a) Use the Central Difference to approximate the bicyclist's velocity at t = 7. Show work clearly and include units in your final answer.

Given the vector function r(t) = (e+²³, 2√1³ +1, 4 arctan(1 − 1) find the speed and the equation of the tangent line to this curve at t = 2, then graph the tangent line. Speed = i(t) =

Consider r(t) = (2t, 3 sint, 3 cost). a. Find the equation of the tangent line to the curve at the point ( b. Find the unit tangent vector T(t) when t = 3 C. Find the length of the curve from t = 1 to t = 3 π 3√/2 3√2. :) } 2' 2 2