Economic

Q: An employee of a delivery company earns 22.50 per hour driving a delivery van in an area where gasoline costs 2.50 per gallon. When the van is driven at a constant speed s (in miles per hour, with ), the van gets miles per gallon. Determine the most economical speed s for a 100-mile trip on an interstate highway. A) The most economical speed is 47.0 mph. B) The most economical speed is 43.0 mph. C) The most economical speed is 22.5 mph. D) The most economical speed is 45.0 mph. E) The most economical speed is 48.0 mph.

Q: Use the graph to sketch the graph of .A)B)C)D)E)

Q: Analyze and sketch a graph of the function . A) B) C) D) E)

Q: Analyze and sketch a graph of the function . A) B) C) D) E) none of the above

Q: Analyze and sketch a graph of the function . A) B) C) D) E)

Q: Sketch the graph of the function given below. Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. A)B)C)D)E)

Q: Sketch the graph of the function below. Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. A)B)C)D)E)

Q: Analyze and sketch a graph of the function . A) B) C) D) E)

Q: The cost C (in millions of dollars) for the federal government to seize p% of a type of illegal drug as it enters the country is modeled by , for . Find the limit of C as. A) 580 B) C) D) E)

Q: A business has a cost (in dollars) of for producing x units. What is the limit ofas x approaches infinity? A) B) $0.90 C) $400.90 D) $400.00 E) $399.10

Q: Sketch the graph of the equation given below. Use intercepts, extrema, and asymptotes as sketching aids.A)B)C)D)E)

Q: Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes. A) B) C) D) E)

Q: Sketch the graph of the function using any extrema, intercepts, symmetry, and asymptotes. A) B) C) D) E)

Q: Find the limit. A) B) C) D) E)

Q: Find the limit. A) B) 7 C) "7 D) E)

Q: Find the limit. A) B) 1 C) 0 D) E)

Q: Find the limit. A) B) C) 1 D) 0 E) does not exist

Q: Use analytic methods to find the limit as for the given function. A) B) C) D) E) does not exist

Q: For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.x 100 101 102 103 104 105 106 f(x)A) 0.6B) 1.666667C) 2.666667D) 1.6E) "0.4

Q: Use a table utility with x-values larger than 10,000 to investigate .What does the table indicate about A) B) C) D) 0 E) does not exist

Q: For the function , use a graphing utility to complete the table and estimate the limit as x approaches infinity.x 100 101 102 103 104 105 106 f(x)A) -0.525B) 1.375C) 0.125D) 2.555E) does not exist

Q: Find the limit: A) 0 B) C) 1 D) "1 E)

Q: Find the limit:A) B) C) 0D) -1E) 1

Q: Match the function with one of the following graphs. A) B) C) D) E)

Q: Find any horizontal asymptotes for the given function. A) B) C) D) E) no horizontal asymptotes

Q: Analytically determine the location(s) of any horizontal asymptote(s). A) B) C) D) E) no horizontal asymptotes

Q: Analytically determine the location of any vertical asymptotes. A) B) C) D) E) no vertical asymptotes

Q: Find all vertical asymptotes for the given function. A) B) C) D) E) no vertical asymptotes

Q: Find any horizontal asymptotes for the given function. A) B) C) D) E) no horizontal asymptotes

Q: Find any vertical asymptotes for the given function. A) B) C) D) E) no vertical asymptotes

Q: Find any horizontal asymptotes for the given function. A) B) C) D) E) no horizontal asymptotes

Q: This problem contains a function and its graph, where Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. A) B) C) D) E)

Q: This problem contains a function and its graph, where Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically. A) B) C) D) E) no vertical asymptote

Q: Analytically determine the location(s) of any horizontal asymptote(s). A) B) C) , D) E) no horizontal asymptotes

Q: Analytically determine the location(s) of any vertical asymptote(s). A) B) C) , D) E) no vertical asymptotes

Q: A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist. Confirm your results analytically. A) B) C) D) E) no horizontal asymptotes

Q: A function and its graph are given. Use the graph to find the vertical asymptotes, if they exist. Confirm your results analytically. A) B) C) D) E) no vertical asymptotes

Q: A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where Confirm your results analytically. A) B) C) D) E) no horizontal asymptotes

Q: A retail sporting goods store estimates that weekly sales and weekly advertising costs are related by the equation . The current weekly advertising costs are $1700, and these costs are increasing at a rate of $130 per week. Find the current rate of change of weekly sales. A) 162,500 dollars per week B) 164,770 dollars per week C) 87,420 dollars per week D) 85,150 dollars per week E) 1,021,570 dollars per week

Q: A baseball diamond has the shape of a square with sides 90 feet long (see figure). A player running from second base to third base at a speed of 30 feet per second is 80 feet from third base. At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.A) -58.2 feet/secondB) -0.2 feet/secondC) -0.7 feet/secondD) -19.9 feet/secondE) -1.9 feet/second

Q: An airplane flying at an altitude of 5 miles passes directly over a radar antenna. When the airplane is 25 miles away (s = 25), the radar detects that the distance s is changing at a rate of 250 miles per hour. What is the speed of the airplane? Round your answer to the nearest integer. A) 255 mi/hr B) 236 mi/hr C) 510 mi/hr D) 128 mi/hr E) 118 mi/hr

Q: Boat docking. Suppose that a boat is being pulled toward a dock by a winch that is 21 ft above the level of the boat deck. If the winch is pulling the cable at a rate of 23 ft/min, at what rate is the boat approaching the dock when it is 28 ft from the dock? Use the figure below. A) B) C) D) E)

Q: A point is moving along the graph of the function such that centimeters per second. Find dy/dt when. A) B) C) D) E)

Q: A point is moving along the graph of the function such that centimeters per second. Find dy/dt for the given values of x. (a) (b) (a) (b) A) B) C) D) E)

Q: The lengths of the edges of a cube are increasing at a rate of 8 ft/min. At what rate is the surface area changing when the edges are 15 ft long? A) 384 ft2/min B) 1440 ft2/min C) 720 ft2/min D) 5760 ft2/min E) 120 ft2/min

Q: Profit. Suppose that the monthly revenue and cost (in dollars) for x units of a product are At what rate per month is the profit changing if the number of units produced and sold is 100 and is increasing at a rate of 10 units per month? A) per month B) per month C) per month D) per month E) per month

Q: The radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rate of change of volume when r = 8 inches. Round your answer to one decimal place. A) 804.2 cubic inches per minute B) 2144.7 cubic inches per minute C) 6434.0 cubic inches per minute D) 2412.7 cubic inches per minute E) 7238.2 cubic inches per minute

Q: Volume and radius. Suppose that air is being pumped into a spherical balloon at a rate of At what rate is the radius of the balloon increasing when the radius is 7 in.? A) B) C) D) E)

Q: Area. The radius, r, of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change of area, A, when the radius is . A) B) C) D) E)

Q: Assume that x and y are differentiable functions of t. Find dx/dt given that , , and A) 1.50 B) 5.33 C) 0.75 D) 24.00 E) 12.00

Q: Given find when x = "9 and A) B) C) D) E)

Q: Assume that x and y are differentiable functions of t. Find dy/dt using the given values. for A) 288 B) 159 C) 318 D) 286 E) 143

Q: Find for the equation by implicit differentiation and evaluate the derivative at the point . A) B) C) D) E) 0

Q: Find dy/dx for the following equation: A) B) C) D) E)

Q: Let x represent the units of labor and y the capital invested in a manufacturing process. When 135,540 units are produced, the relationship between labor and capital can be modeled by . Find the rate of change of y with respect to x when . A) -2 B) 0 C) 3 D) -7 E) 5

Q: Find implicitly and explicitly(the explicit functions are shown on the graph) and show that the results are equivalent. Use the graph to estimate the slope of the tangent line at the labeled point. Then verify your result analytically by evaluating at the point. A) B) C) D) E)

Q: Find the rate of change of x with respect to p. A) B) C) D) E)

Q: Find the slope of the graph at the given point. A) 2 B) 0 C) 1 D) 3 E) 5

Q: Find the slope of the graph at the given point. A) 0 B) 3 C) 5 D) 4 E) 7

Q: Find for the equation . A) B) C) D) E)

Q: Find implicitly for A) B) C) D) E)

Q: A brick becomes dislodged from the Empire State Building (at a height of 1025 feet) and falls to the sidewalk below. Write the position s(t), velocity v(t), and acceleration a(t) as functions of time. A) ; ; B) ; ; C) ; ; D) ; ; E) ; ;

Q: Find the second derivative for the function and solve the equation . A) 0 B) 7 C) no solution D) "7 E)

Q: Find the second derivative for the function and solve the equation . A) "1 B) 4 C) 0 D) 18 E) 20

Q: Find the indicated derivative. Find A) B) C) D) E)

Q: Find the value for the function . A) 734,208 B) 430,080 C) 221,185 D) 430,081 E) 3,403,776

Q: Find the third derivative. A) B) C) D) E)

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