Chapter 4 5 6 Cale Short Answer 3 2 1. An object is moving in a straight line with its position at time 3 seconds given by 3(3) = 2'! + 153 + 24; + 6 where 5 is measured in metres. For what times 3 is the object moving in the negative direction? x) _ r: + 2r+ 3 ' 2 2. Let 2}: + 39" "' 1 . What is the equation of the horizontal asymptote of r) '? From what direction does 3133' approach the asymptote as I tends towards +00? r 2 3. Let f (x) 2 I + 2D?\" 1 .For what values of K is x) concave down? 2 3 4. Let x) : 73(2x+ 41' . For what values of 1' is r.) concave up? 5. Give an example of a function for which the graph is concave up for x 0. 6. Determine the absolute extrema ofthe function x) = (\"T 33'2x on the interval '1 5 I 5 3. 7. Differentiate the rnction le = ~.' 3 '3'3'5 X _ 9x . 5T 8. Determine the equation for the tangent to the curve 3" = tanr at the point withx-coordinate 3 . r '3' } A ll A73 _. _. I ' 9. A and 5' forrnaright angle. = 8 and = 1. Determine } } } 10. Explain how the vector C (going from the head of B to the head of A ) can be written in terms of vectors } } zqandB. 11. Is 3 A = m, m being any real number, possible? Explain. A 12. = 6, = 7 and the angle between A and is 30. Determine a unit vector in the opposite direction of B 13. A parallelogram is defined in R' by the vectors CA = (1, 3, -8) and OF = (3, 5, 1). Determine the coordinates of the vertices. Explain briefly your reasoning for the points. 14. In the set: {(1, 0), {0, a)}, what must a be for this to span R'? Why? 15. The set {(1, 0), (1, 1), (0, 1)} spans R'. Which vectors could be removed while still preserving the set spanning R. Explain your reasoning