The relationship between the number of decibels and the intensity of a sound I in
watts per square centimeter is given by . Find the rate of change in
the number of decibels when the intensity is watt per square centimeter. Round
your answer to the nearest decibel.
A) 434 decibels per watt per square cm
B) 43,429 decibels per watt per square cm
C) 4343 decibels per watt per square cm
D) 434,294 decibels per watt per square cm
E) 4345 decibels per watt per square cm
Use a table of integrals with forms involving a + bu to find
A)
B)
C)
D)
E)
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
Find the slope of the line passing through the given pair of points.
and
A) “8
B)
C) “7
D) 0
E) The slope is undefined.
Use Lagrange multipliers to maximize the function subject to
the following constraint:
Assume that x, y, and z are positive.
A)
B)
C)
D)
E) no absolute maximum
Solve for y in two ways.
A)
B)
C)
D)
E)
Find for the equation .
A)
B)
C)
D)
E)
Evaluate without using a calculator.
A)
B)
C)
D)
E) 0
Find the slope of the line passing through the given pair of points.
and
A) “18
B)
C) 3
D)
E) The slope is undefined.
Find the indefinite integral.
A)
B)
C)
D)
E) none of the above
Analyze and sketch a graph of the function .
A)
B)
C)
D)
E)
A medical researcher wants to determine the concentration C (in moles per liter) of a
tracer drug injected into a moving fluid with flow R (in liters per minute). Solve this
problem by considering a single-compartment dilution model (see figure). Assume that
the fluid is continuously mixed and that the volume V (in liters) of fluid in the
compartment is constant.
If the tracer is injected instantaneously at time , then the concentration of the fluid
in the compartment begins diluting according to the differential equation
when (a) Solve this differential equation to find the
concentration as a function of time. (b) Find the limit of as
A) a. b. 1
B) a. b. 0
C) a. b. 2
D) a. b. 0
E) a. b. 1
Find the x-values (if any) at which f(x) is not continuous and identify whether they are
removable or nonremovable.
A) x = 1 is a removable discontinuity
B) x = 1 is a nonremovable discontinuity
C) x = -1 is a removable discontinuity
D) x = -1 is a nonremovable discontinuity
E) f(x) has no discontinuities
Use the given information to write an exponential equation for y. Does the function
represent exponential growth or exponential decay?
A)
B)
C)
D)
A manufacturer charges $70 per unit for units that cost $60 to produce. To encourage
large orders from distributors, the manufacturer will reduce the price by $0.02 per unit
for each unit in excess of 100 units. (For example, an order of 101 units would have a
price of $69.98 per unit, and an order of 102 units would have a price of $69.96 per
unit.) This price reduction is discontinued when the price per unit drops to $64. Express
the price per unit as a function of the order size.
A)
B)
C)
D)
E)
Determine the open intervals on which the graph of is concave
downward or concave upward.
A) concave upward on ; concave downward on
B) concave downward on
C) concave upward on
D) concave downward on ; concave upward on
E) concave upward on ; concave downward on
A function and its graph are given. Use the graph to find the horizontal asymptotes, if
they exist. Confirm your results analytically.
A)
B)
C)
D)
E) no horizontal asymptotes
Sketch the region whose area is given by the definite integral and then use a geometric
formula to evaluate the integral.
A)
B)
C)
D)
E) none of the above
Write the logarithmic equation as an exponential equation.
A)
B)
C)
D)
E)
Write the following expression as a logarithm of a single quantity.
A)
B)
C)
D)
E)
Find the point on the graph of that is closest to the point (3, 0.5). Round your
answer to two decimal places.
A) (1.14, 1.30)
B) (1.44, 2.07)
C) (1.82, 3.31)
D) (1.00, 1.00)
E) (0.91, 0.83)
Given and , find
A)
B)
C)
D)
E)
Sketch the graph of the function .
A)
B)
C)
D)
E)
Evaluate the expression .
A) 243
B) 3
C) 9
D) 11
E) 13
A small business purchases a piece of equipment for $1030. After 10 years, the
equipment will be outdated, having no value. Write a linear equation giving the value V
of the equipment in terms of time t in years,
A) V = “103t 1030
B) V = 103t + 1030
C) V = 103t 1030
D) V = “103t + 1030
E) V = “103t + 103
A deposit of 800 is made each month in an account that earns 8.4% interest,
compounded monthly. The balance in the account after n months is given by
. Find the balance after 20 years by computing the 240th
term of the sequence. Round your answer to two decimal places.
A) $696,946.54
B) $1,018,546.54
C) $24,073.84
D) $343,954.07
E) $1,125.60
Estimate the surface area of the golf green shown in the figure using the midpoint rule.
A) 780
B) 156
C) 1404
D) 1502
E) 524
Find the indefinite integral and check the result by differentiation.
A)
B)
C)
D)
E) none of the above
Find the differential dy of the function .
A)
B)
C)
D)
E)
Use a table of integrals to find the indefinite integral .
A)
B)
C)
D)
E)
Suppose the sales S (in billions of dollars per year) for Proctor & Gamble for the years
1999 through 2004 can be modeled by
where t represents the year. During
which year were the sales increasing at the lowest rate?
A) Sales are increasing at the lowest rate in the year 2004.
B) Sales are increasing at the lowest rate in the year 1999.
C) Sales are increasing at the lowest rate in the year 2000.
D) Sales are increasing at the lowest rate in the year 2002.
E) Sales are increasing at the lowest rate in the year 2001.
Use the graph of below to sketch the graph of the following function:
A)
B)
C)
D)
E)
Determine whether the improper integral diverges or converges. Evaluate the integral if
it converges.
A) converges to 0
B) converges to 3
C) converges to
D) diverges to
E) diverges to
Use integration to find a general solution of the differential equation .
A)
B)
C)
D)
E)
Find the period of the trigonometric function.
A)
B)
C)
D)
E)