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Q: Suppose the number y of medical degrees conferred in the United States can be modeled by for , where t is the time in years, with corresponding to 1975. Use the test for increasing and decreasing functions to estimate the years during which the number of medical degrees is increasing and the years during which it is decreasing. A) The number of medical degrees is increasing from 1975 to 1992 and 2000 to 2005, and decreasing during 1992 to 2000. B) The number of medical degrees is increasing from 1975 to 1991 and 1999 to 2005, and decreasing during 1991 to 1999. C) The number of medical degrees is increasing from 1975 to 1992 and 1999 to 2005, and decreasing during 1992 to 1999. D) The number of medical degrees is increasing from 1975 to 1993 and 1999 to 2005, and decreasing during 1993 to 1999. E) The number of medical degrees is increasing from 1975 to 1992 and 1998 to 2005, and decreasing during 1992 to 1998.

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Q: Find the open intervals on which the function is increasing or decreasing. A) The function is increasing on the interval and decreasing on the interval . B) The function is increasing on the interval and decreasing on the interval . C) The function is increasing on the interval and decreasing on the interval . D) The function is increasing on the interval and decreasing on the interval . E) The function is increasing on the interval and decreasing on the interval .

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Q: Identify the open intervals where the function is increasing or decreasing. A) decreasing: ; increasing: B) increasing: ; decreasing: C) increasing: ; decreasing: D) increasing: ; decreasing: E) decreasing for all x

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Q: The variable cost for the production of a calculator is 16.25 and the initial investment is 530,000. Use differentials to approximate the change in the cost C for a one-unit increase in production when , where x is the number of units produced. A) 1300000.00 dollars B) 17.25 dollars C) 1301000.00 dollars D) 16.25 dollars E) 26.25 dollars

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Q: Compare dy and for at x = 0 with dx = 0.09. Give your answers to four decimal places.A) dy = 0.0200 ; = -0.0002B) dy = -0.0100 ; = "0.0001C) dy = -0.0300 ; = 0.0000D) dy = 0.0000 ; = 0.0001E) dy = 0.0200 ; = 0.0000

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Q: Compare dy and for at x = 1 with dx = 0.05. Give your answers to four decimal places. A) B) C) D) E)

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Q: Find the differential dy of the function . A) B) C) D) E)

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

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

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

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

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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

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

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

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

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

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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

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

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

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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)

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

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

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

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Q: A population of bacteria is introduced into a culture. The number of bacteria P can be modeled by where t is the time (in hours). Find the rate of change of the population when t = 2. A) B) C) D) E)

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Q: Find the marginal revenue for producing x units. (The revenue is measured in dollars.) A) B) C) D) E)

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Q: The graph shows the number of visitors V to a national park in hundreds of thousands during a one-year period, where t = 1 represents January. Estimate the rate of change of V over the interval . Round your answer to the nearest hundred thousand visitors per year. A) 176.92 hundred thousand visitors per year B) 328.57 hundred thousand visitors per year C) 166.67 hundred thousand visitors per year D) 383.33 hundred thousand visitors per year E) 766.67 hundred thousand visitors per year

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Q: Find the derivative of the function. A) B) C) D) E) none of the above

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Q: Find the derivative of the function. A) B) C) D) E) none of the above

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Q: Identify a function that has the given characteristics and then sketch the function. A) B) C) D) E)

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Q: Find the derivative of the following function using the limiting process. A) B) C) D) E) either B or D

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