Exponential and Trig Derivatives 1. Find the equation of the tangent to the function f(x) = exsinx at x = 2 2. Determine the maximum length of a rod that can be taken from a hallway that is 2m wide around a corner to a perpendicular hallway that is 3m wide. Introduction to Vectors 1. Determine the resultant of the following vectors: a) 4(3,8,1) 9(2,7 4) b) a vector 7cm long and the vector 12cm long at an angle of 34" clockwise from the first vector. 2. Determine the Northern and Western components of the boat going 82 km/h at a bearing of 2830 3. Is (5, 6,4) on the plane determined by the span of {(4,9,2), (3,1,2)}? 4. What is a linear combination and how does it relate to a spanning set? 5. Sketch the parallelepiped formed by the vectors (3,5,2), (6,1,3), (4,3,8). Applications of Vectors 1. Determine the angle between the vectors a" = (8,3,5) and b" = (2,9,4). 2. How much horizontal work is done if Mrs. Bethany is pulling a trolley on a flat surface for 70 m and she is pulling with a force of 80 N along the handle, which is at an angle of 43" above the horizontal? 3. Determine the normal of the vectors a> : (8,3,5) and b" = (2,9, 4) 4. Determine the magnitude ofthe torque on a nut if the wrench is 21cm long and if the 50 N force is applied at an angle of 70 to the wrench. 5. Find the scalar projection of the vector a" = (3,2,6) on b" = (2,0,8). 6. Determine the vector projection of the vector (1" = (9,2,6) on b" = (3,2,8). 7. At what bearing should a ship aim in order to travel at a bearing of 98'J if the 23 km/h wind is pushing the boat at a bearing of 072 and the ship's propellers are pushing it at a speed of 89 km/h? 8. What is an equilibrant? 9. A mass of 90 kg is suspended from a ceiling by two lengths of rope that make angles of 40" and 60" with the ceiling. Determine the tension in each of the ropes