Exam 4: Section 5: Applications of Differentiation

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Find the limit. Find the limit.

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Sketch the graph of the relation Sketch the graph of the relation   using any extrema, intercepts, symmetry, and asymptotes. using any extrema, intercepts, symmetry, and asymptotes.

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Find the limit. Find the limit.

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A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded for the first two minutes is given by A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded for the first two minutes is given by   . Find   . . Find A heat probe is attached to the heat exchanger of a heating system. The temperature T (in degrees Celsius) is recorded t seconds after the furnace is started. A model for the data recorded for the first two minutes is given by   . Find   . .

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Match the function Match the function   with one of the following graphs. with one of the following graphs.

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Find the limit. Find the limit.

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For the function For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity.  , use a graphing utility to complete the table and estimate the limit as x approaches infinity. For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

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Find the limit. Find the limit.

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Sketch the graph of the relation Sketch the graph of the relation   using any extrema, intercepts, symmetry, and asymptotes. using any extrema, intercepts, symmetry, and asymptotes.

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Match the function Match the function   with one of the following graphs. with one of the following graphs.

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A business has a cost of A business has a cost of   for producing x units. The average cost per unit is   Find the limit of   as x approaches infinity. for producing x units. The average cost per unit is A business has a cost of   for producing x units. The average cost per unit is   Find the limit of   as x approaches infinity. Find the limit of A business has a cost of   for producing x units. The average cost per unit is   Find the limit of   as x approaches infinity. as x approaches infinity.

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A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as   . Find   . Round your answer to two decimal places. . Find A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as   . Find   . Round your answer to two decimal places. . Round your answer to two decimal places.

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Sketch the graph of the function Sketch the graph of the function   using any extrema, intercepts, symmetry, and asymptotes. using any extrema, intercepts, symmetry, and asymptotes.

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Find the point on the graph of the function Find the point on the graph of the function   that is closest to the point   . that is closest to the point Find the point on the graph of the function   that is closest to the point   . .

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Find the limit. Find the limit.

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Find the limit. Find the limit.

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Find the point on the graph of the function Find the point on the graph of the function   that is closest to the point   . Round all numerical values in your answer to four decimal places. that is closest to the point Find the point on the graph of the function   that is closest to the point   . Round all numerical values in your answer to four decimal places. . Round all numerical values in your answer to four decimal places.

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For the function For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity.  , use a graphing utility to complete the table and estimate the limit as x approaches infinity. For the function   , use a graphing utility to complete the table and estimate the limit as x approaches infinity.

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A rectangular page is to contain A rectangular page is to contain   square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

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The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln. The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln.   Find   . Find The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln.   Find   . .

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