Find the distance between the points and . Round your answer to the nearest
hundredth.
A) 25.00
B) 2.65
C) 5.00
D) 14.87
E) 4.58
Find the relative maxima, and use a graphing utility to check your results.
A)
B)
C)
D)
E) does not exist
The revenue from a manufacturing process (in millions of dollars per year) is projected
to follow the model for 10 years. Over the same period of time, the
cost (in millions of dollars per year) is projected to follow the model ,
where t is the time (in years). Approximate the profit over the 10-year period, beginning
with t = 0. Round your answer to two decimal places.
A) million
B) million
C) million
D) million
E) million
Two models, and , are given for revenue (in billions
of dollars per year) for a large corporation. Both models are estimates of revenues for
2007 through 2011, with t = 7 corresponding to 2007. Which model is projecting the
greater revenue? How much more total revenue does that model project over the
five-year period?
A) The model projects greater revenue than . billion
B) The model projects greater revenue than . billion
C) The model projects greater revenue than . billion
D) The model projects greater revenue than . billion
E) The model projects greater revenue than . billion
Find the indefinite integral of the following function.
A)
B)
C)
D)
E)
A body assimilates a 16-hour cold tablet at a rate modeled by ,
where t is measured in milligrams per hour and t is the time in hours. Use
Simpson’s Rule with n = 16 to estimate the total amount of the drug absorbed into the
body during the 16 hours.
A) 58.88
B) 34.88
C) 54.33
D) 46.88
E) 64.90
Find if .
A)
B)
C)
D)
E)
Match the function with one of the following graphs.
A)
B)
C)
D)
E)
Because of the forces caused by its rotation, a planet is actually an oblate ellipsoid
rather than a sphere. The equatorial radius is 3963 miles and the polar radius is 3953
miles. Find an equation of the ellipsoid. Assume that the center of a planet is at the
origin and the xy- trace corresponds to the equator.
A)
B)
C)
D)
E)
For the given function, find all critical numbers.
A)
B) and
C) and
D) and
E) and
A model for the ability M of a child to memorize, measured on a scale from 0 to 10, is
where t is the child’s age in years. Find the average value
predicted by the model for a child’s ability to memorize between first and second
birthdays. Round your answer to three decimal places.
A) 3.318
B) 2.218
C) 4.118
D) 1.318
E) 2.018
Determine whether the function is a solution of the differential equation
.
A) Solution
B) Not a solution
A sector of a circle is the region bounded by two radii of the circle and their intercepted
arc (see figure).
For a circle of radius the area of a sector of the circle with central angle (measured
in radians) is given by . A sprinkler system on a farm is set to spray water
over a distance of feet and rotates through an angle of . Use the above given
information to find the area of the region. Round your answer to two decimal places.
A) 2828.57
B) 257.14
C) 2700.00
D) 1414.29
E) 9900.00
Find the derivative of the following function.
A)
B)
C)
D)
E)
Use the Midpoint Formula repeatedly to find the three points that divide the segment
joining and into four equal parts.
A)
B)
C)
D)
E)
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
Find the equilibrium point for the following supply and demand functions below, where
p is price per unit and q is the number of units produced and sold. Demand:
Supply:
A)
B)
C)
D)
E)
Find the marginal profit for producing x units. (The profit is measured in dollars.)
A)
B)
C)
D)
E)
Assume the population P (in millions) of the United States from 1992 through 2005 can
be modeled by the exponential function , where t is the time in
years, with t = 2 corresponding to1992. Use the model to estimate the population in the
year 2007. Round your answer to the nearest million.
A) 7022 million
B) 4372 million
C) 11,277 million
D) 657 million
E) 7021 million
Determine whether the given function is continuous. If it is not, identify where it is
discontinuous and which condition fails to hold. You can verify your conclusions by
graphing the function with a graphing utility, if one is available.
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A large corporation starts at time to invest part of its profit at a rate of dollars
per year in a fund for future expansion. Assume that the fund earns percent interest
per year compounded continuously. The rate of growth of the amount in the fund is
given by where when and is in decimal form. Solve this
differential equation for as a function of .
A)
B)
C)
D)
E)
Write the equation of the line tangent to the curve
A)
B)
C)
D)
E)
Find .
A)
B)
C)
D)
E)
Determine the graph whose area (the shaded region) is represented by the integral.
A)
B)
C)
D)
E)
Find all vertical asymptotes for the given function.
A)
B)
C)
D)
E) no vertical asymptotes
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 t-value at which x
is maximum. Round your answer to two decimal places.
A) 0 hours
B) 2.24 hours
C) 894.43 hours
D) 4.24 hours
E) 5.46 hours
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 .
A) 31.03 units per dollar
B) 1.75 units per dollar
C) 7.01 units per dollar
D) 3.63 units per dollar
E) 7.76 units per dollar
Evaluate the definite integral .
A) 3
B) “3
C)
D)
E)
Find the derivative of the function.
A)
B)
C)
D)
E)
Find the of .
A)
B)
C)
D)
E)
Sketch the graph of the function using any extrema, intercepts, symmetry,
and asymptotes.
A)
B)
C)
D)
E)
Evaluate and for the function at the point . Round your
answer to two decimal places.
A) 4.03 and 1.19
B) 3.53 and 1.19
C) 3.88 and 5.82
D) 4.03 and 0.69
E) 3.88 and 5.82