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The graph of f is shown in the figure. Sketch a graph of the derivative of f.
A)
B) The derivative of f does not exist.
C)
D)
E)
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
Identify u and dv for finding the integral using integration by parts.
A)
B)
C)
D)
E)
Find the derivative of the function.
A)
B)
C)
D)
E)
Evaluate the definite integral dx. Round your answer to three decimal places.
A) 6.144
B) 7.207
C) 4.541
D) 5.644
E) 4.881
Find the midpoint of the line segment joining the points and . Round your
answer to the nearest hundredth.
A)
B)
C)
D)
E) none of these choices
Describe the level curves for the function for the c-values given by
.
A)
B)
C)
D)
E)
Suppose the resident population of South Carolina (in thousands) was 4020 in 2000 and
4257 in 2007. Assume that the relationship between the population and the year is
linear. Let represent 2000. Estimate the population in 2004 by using linear model
for the given data. Round your answer to the nearest thousand residents.
A) 4336 thousand residents
B) 3885 thousand residents
C) 4122 thousand residents
D) 4155 thousand residents
E) 4392 thousand residents
Analytically determine the location(s) of any horizontal asymptote(s).
A)
B)
C)
D)
E) no horizontal asymptotes
Assume that the number (in millions) of cellular telephone subscribers in the United
States from 1996 through 2005 is given in the following table. Use a graphing utility to
graph a line plot of the given data. Describe any trends that appear within the last four
years.
A)
The number of subscribers appears to be decreasing.
B)
The number of subscribers appears to be increasing.
C)
The number of subscribers appears to be constant.
D)
The number of subscribers appears to be decreasing.
E)
The number of subscribers appears to be increasing linearly.
Find the indefinite integral.
A)
B)
C)
D)
E)
How much more interest will be earned if $4000 is invested for 7 years at an annual rate
of 12% compounded continuously, instead of at 12% compounded quarterly?
A) $38.58
B) $75.18
C) $113.76
D) $1791.71
E) $1866.89
The graph of f is shown in the figure. Sketch a graph of the derivative of f.
A)
B)
C)
D)
E)
Find the average value of the function over the given interval.
on [0,1]
A)
B)
C)
D)
E)
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
Estimate the slope of the line from the graph.
A)
B) 6
C)
D) "6
E) None of the above
The rate of change in sales (in thousands of units) of a new product is proportional to
the difference between and at any time (in years), where is the maximum
number of units of the new product available. When Write and solve the
differential equation for this sales model.
A)
B)
C)
D)
E)
A firm can produce 100 units per week. If its total cost function is
dollars, and its total revenue function is dollars, find the maximum
profit.
A) $6319
B) $1900
C) $8236
D) $6921
E) $2806
Evaluate the definite integral . Round your answer to three decimal places.
A) 828.111
B) 207.823
C) 118.290
D) 207.811
E) 79.245
Find the derivative of the given function. Simplify and express the answer using
positive exponents only.
A)
B)
C)
D)
E)
The average monthly precipitation P (in inches), including rain, snow, and ice, for
Sacramento, California can be modeled by
where is the time (in months), with corresponding to January. Find the total
annual precipitation for Sacramento.
A) in.
B) in.
C) in.
D) in.
E) in.
Determine whether the function is a solution of the differential equation
.
A) Solution
B) Not a solution
Compare dy and for at x = "1 with dx = 0.07. Give your answers
to four decimal places.
A)
B)
C)
D)
E)
Find the indefinite integral and check your result by differentiation.
A)
B)
C) 12
D)
E)
Identify u and for the integral .
A) and
B) and
C) and
D) and
E) and
Suppose the mean height of American women between the ages of 30 and 39 is 68.5
inches, and the standard deviation is 2.7 inches. Use a symbolic integration utility to
approximate the probability that a 30-to 39-year-old woman chosen at random is
between 5 and 6 feet tall.
A) 0.1772
B) 0.9017
C) 0.5707
D) 0.8547
E) 0.4257
A company manufactures two types of wood-burning stoves: a freestanding model and
a fireplace-insert model. The cost function for producing x freestanding and y
fireplace-insert stoves is . Find the marginal costs (
and ) when and . Round your answers to two decimal
places.
A)
B)
C)
D)
E)
Use the regression capabilities of a graphing utility or a spreadsheet to find the least
squares regression line for the given points.
A)
B)
C)
D)
E)
Analyze and sketch a graph of the function .
A)
B)
C)
D)
E)
Use a graphing utility to graph the function .
A)
B)
C)
D)
E)
Approximate the sum of the convergent series using three terms. Estimate the
maximum error of your approximation. Round your answers to four decimal places.
A) The approximate value is 2.1854. The maximum error of your approximation is
0.0588.
B) The approximate value is 1.1620. The maximum error of your approximation is
0.0556.
C) The approximate value is 2.1676. The maximum error of your approximation is
0.0721.
D) The approximate value is 3.1591. The maximum error of your approximation is
1.0527.
E) The approximate value is 1.1644. The maximum error of your approximation is
0.0573.
