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Find the limit.
A)
B) 1
C) 0
D)
E)
Use the integration to find the general solution of the differential equation .
A)
B)
C)
D)
E)
Find the median of the exponential probability density function over the
interval .
A) 1.213
B) 0.693
C) 0.396
D) 1.061
E) 0.875
Find the area of the shaded region.
A)
B)
C)
D)
E)
Solve the triangle for the indicated angle.
A) angle 40
B) angle 90
C) angle 140
D) angle 50
E) angle 130
Find the x-values (if any) at which the function is not continuous.
Which of the discontinuities are removable?
A) no points of discontinuity
B) (not removable), (removable)
C) (removable), (not removable)
D) no points of continuity
E) (not removable), (not removable)
Write the expression as the logarithm of a single
quantity.
A)
B)
C)
D)
E)
Find the limit of the following sequence.
A) "1
B) 1
C)
D) 2
E) The sequence diverges.
Find the particular solution that satisfies the differential equation and
initial condition .
A)
B)
C)
D)
E)
Find the particular solution that satisfies the initial condition. ;
Initial Condition: when
A)
B)
C)
D)
E)
Determine whether the statement is true or false. If it is false, explain why or give an
example that shows it is false. Data that are modeled by have a positive
correlation.
A) True
B) False; The data modeled by have a positive correlation.
Assume that the rate of change in y is proportional to y. Solve the resulting differential
equation and find the particular solution that passes through the points
A)
B)
C)
D)
E)
Evaluate the improper integral if it converges, or state that it diverges.
A)
B)
C)
D)
E) diverges
Approximate using a calculator (set for radians). Round answers to two decimal places.
A) 0.78
B) 0.14
C) "0.62
D) "0.99
E) "1.00
Find the slope of the line passing through the pair of points.
A)
B) -
C)
D) -
E) None of the above
When predicting population growth, demographers must consider birth and death rates
as well as the net change caused by the difference between the rates of immigration and
emigration. Let be the population at time and let be the net increase per unit
time due to the difference between immigration and emigration. So, the rate of growth
of the population is given by is constant. Solve the differential equation
to find as a function of .
A)
B)
C)
D)
E)
Find the third Taylor polynomial at for the given function.
A)
B)
C)
D)
E)
For a person at rest, the velocity v (in liters per second) of air flow into and out of the
lungs during a respiratory cycle is given by , where t is the time in seconds.
Inhalation occurs when and exhalation occurs when . Find the time for one
full respiratory cycle.
A) seconds
B) seconds
C) 18 seconds
D) seconds
E) 9 seconds
The capitalized cost of an asset is given by where is the
original investment, is the time in years, is the annual interest rate compounded
continuously, and is the annual cost of maintenance (in dollars). Find the
capitalized cost of an asset (a) for 5 years, (b) for 10 years, and (c) forever.
A) a. For $253,901.30 b. For $807,922.43 c. For
$4,466,666.67
B) a. For $453,901.30 b. For $807,922.43 c. For
$1,466,666.67
C) a. For $453,901.30 b. For $2807,922.43 c. For
$4,466,666.67
D) a. For $453,901.30 b. For $807,922.43 c. For
$4,466,666.67
E) a. For $453,901.30 b. For $807,922.43 c. For
$466,666.67
Use a double integral to find the volume of the solid bounded by the graphs of the
equations .
A)
B)
C)
D)
E)
Solve the triangle for the indicated side and angle.
A) angle 60 side
B) angle 30 side
C) angle 45 side
D) angle 60 side
E) angle 40 side
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
Find the derivative of the following function.
A)
B)
C)
D)
E)
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)
If , is y a function of x?
A) Yes
B) No
Find of the functions .
A)
B)
C)
D)
E)
Locate any relative extrema and inflection points of the function .
A) relative minimum at ; inflection point at
B) relative minimum at ; no inflection points
C) no relative maximum or minimum; inflection point at
D) no relative extrema or inflection points.
E) relative maximum at ; inflection point at
Average costs. Suppose the average costs of a mining operation depend on the number
of machines used, and average costs, in dollars, are given by
, where x is the number of machines used. How many
machines give minimum average costs?
A) Using 15 machines gives the minimum average costs.
B) Using zero machines gives the minimum average costs.
C) Using 25 machines gives the minimum average costs.
D) Using 30 machines gives the minimum average costs.
E) Using 35 machines gives the minimum average costs.
Find two values of q that satisfy the equation below. Give values of q in radians
. Do not use a calculator. sin q =
A)
B)
C) ,
D)
E)
Determine the convergence or divergence of the sequence . If the sequence
converges, use a symbolic algebra utility to find its limit.
A) 7
B) 1
C) 2
D)
E) The sequence diverges.
Sketch the graph of the equation.
A)
B)
C)
D)
E) None of the above
