MATH 212 Midterm: MATH212_ALL-SECTIONS_SPRING2012_0000_MID_EXAM_1

A -(2, 4,6, 8) be a set in the universe U (1, 2, 3, 4, 5, 6, 7,8, 9, 10). Find the complement of A. Tro complomant of A 34. Identify the domain and range of the following relation: ((-4, 5).(3, 7). (2, 8), (5, 7) Does the relation represent a function? Why or why not? t is a nction,s proven by te verial life , 500, 12,500, l62,500 35. Identify a pattern and find the next three terms in the pattern. 4, 20, 100, 500, 36. Write an algebraic model that represents three times the difference of x and y. 37. Evaluate the algebraic expression by substituting the number for each variable: 3x- 4y-2y3 for x =-2 and y-3 38. Identify the property illustrated by each equation (word bank: Associative Property itution, Distributive Property Symmetric Property) b. (x+y)+z=x+(y + z) c. -8(a+b) -8a -8b d. If x = 2 and 4 + x-y, then 4 + 2-y 39. Is the inequality always, sometimes, or never true? 6(2x + 4)-8x+2 S 4x+ 26 40. Use the quadratic formula x =-m4ac to solve for x: 2x2 +4x-3-0

Use the function to answer the following (1-6): Assuming that f(x) is a one-to-one function (you can see that it passes the horizontal line test if you graph it with a graphing utility) find its inverse f -1(x), and then identify the domain and range of f(x) and f-1(x). Assuming that show that f(f-1(x))=f-1(f(x))=x Find the derivatives of f(x) and f-1(x). Show that According with properties of inverse functions, if the point (a, b) is on the graph of f(x).then the point (b, a) should be on the graph of Check if this property is being satisfied for the points (1,2) and (2,1) respectively. Find the slopes and the equations of the tangent lines to the graphs of f(x) and f-1(x) at the points (1, 2) and (2, 1) respectively. What is the relationship between the two slopes? Suppose that the differentiable function y = f(x) has an inverse, and the graph of f passes through the point (5, 3) and has a slope of there. Find the slope and the equation of the tangent line to the graph of at the point (3,5). Suppose the inverse o f a differentiable function y = f(x) passes through the origin with slope Find the slope and the equation o f the tangent line to the graph of the function at the origin.

..1 Verizon令 3:36 PM webassign.net The cost function for production of a commodity is 9+2x-0.062+0.000 (a) Find C(100) Interpret coo O This is the rate at which the production level is decreasing with respect to the cost when x = 100. O This is the cost of making 100 items. O This is the number of items that must be produced before the costs reach 100 O This is the rate at which costs are increasing with respect to the production level when x = 100. O This is the amount of time, in minutes, it takes to produce 100 items (b) Find the actual cost of producing the 101st item. (Round your answer to the nearest cent.) The position function of a particle is given below When does the particle reach a velocity of 5 m/s? Need Help? If a ball is given a push so that it has an initial velocity of 6 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation (a) Find the velocity after 2 seconds. m/s (b) How long does it take for the velocity to reach 40 m/s? (Round your answer to two decimal places.)