Exam 1: Functions, graphs, and Limits
Exam 1: Functions, graphs, and Limits427 Questions
Exam 2: Differentiation84 Questions
Exam 3: Applications of the Derivative122 Questions
Exam 4: Exponential and Logarithmic Functions122 Questions
Exam 5: Integration and Its Applications88 Questions
Exam 6: Techniques of Integration46 Questions
Exam 7: Functions of Several Variables113 Questions
Exam 8: Trigonometric Functions60 Questions
Exam 9: Probability and Calculus36 Questions
Exam 10: Series and Taylor Polynomials104 Questions
Exam 11: Differential Equations77 Questions
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Minimum cost.From a tract of land,a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle.Suppose that the fence for the outside boundary costs $7 per foot and the fence for the middle costs $4 per foot.If each lot contains 5000 square feet,find the dimensions of each lot that yield the minimum cost for the fence.
(Multiple Choice)
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The average time between incoming calls at a switchboard is 3 minutes.If a call has just come in,the probability that the next call will come within the next t minutes is
Find the probability that the next call will come within the next
minute.Round your answer to two decimal places.
(Multiple Choice)
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Use analytic methods to find the limit as
for the given function.
(Multiple Choice)
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The red figure is translated to a new position in the plane to form the blue figure.Find the vertices of the transformed figure from the following graph.(In case your exam is printed in black and white - the red figure has one vertex at (0,0)).
(Multiple Choice)
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Find the second derivative for the function
and solve the equation
(Multiple Choice)
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The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by
During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years?
(Multiple Choice)
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Locate any relative extrema and inflection points of the function
Use a graphing utility to confirm your results.
(Multiple Choice)
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What percent of a present amount of radioactive radium
will remain after 900 years? The half-life of radium is 1,600 years.
(Multiple Choice)
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Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
If
,then
(True/False)
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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
(Multiple Choice)
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Analytically determine the location(s)of any horizontal asymptote(s).
(Multiple Choice)
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The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when
inches.Round your answer to one decimal place.
(Multiple Choice)
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Medication.The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by
Find the maximum value of x.Round your answer to two decimal places.
(Multiple Choice)
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Find the x-values (if any)at which f(x)is not continuous and identify whether they are removable or nonremovable.
(Multiple Choice)
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