Final Exam MCV4U Short Answer 1. What does the rate of change of the position function represent? 2. Sketch the graph of any function that satisfies the following conditions: lim Ax) = 4 lim f(x) = 4 AZ) = 1 x-2 , and * 2* lim 1(x) - x 3.Determine, using the properties of limits, VAX) lim A(x) = 9 given *--9 4.Explain a general approach to determining a limit. An =- Vx2 - 5 4x2 - 5 5.Use a graphing calculator to graph the function and to estimate *+-3 Then, determine the limit by substitution. 6. The graph of f(x) is shown below. Use the graph to determine the values of x for which 7 (X) = . (Hint: the values are integers.) Ax) = 2x 7.Determine the maximum function value for the function (x + 2) on the interval [ - 1, 2]. 8. If A21) >Axal for every *1 2 72 then what is the behaviour of /(? 9.Explain mathematically why there are no points for the function f(x) = -6" where the tangent is horizontal 10.Determine the equation for the tangent to the curve J' = -fan. at the point with x-coordinate B F 11. Name a vector opposite to ABA 12. = 3, =5 and the angle formed by A and B is 30. A + B = ? B A+ B 13.Determine the angle between the line segments connecting the origin with the point (4, 5) and the origin with the point (-2, 2). 14.Determine the unit vector that is normal to the plane " = (1, -4, 3 ) + 8( 2, 0, - 4 ) + 1(0, 3, 1), s, 1 = R. 15. Determine the distance form the origin to the line -4X + 7 - 8 = 0