Volume and radius. Suppose that air is being pumped into a spherical balloon at a rate
of At what rate is the radius of the balloon increasing when the radius is 7
in.?
A)
B)
C)
D)
E)
Find all relative extrema of the function . Use the Second
Derivative Test where applicable.
A) relative min:
B) relative max:
C) no relative max
D) no relative min
E) both A and C
F) both B and D
Find the intercepts of the plane given by .
A) The -intercept is . The -intercept is . The -intercept is .
The -intercept is .
The -intercept is .
The -intercept is .
B) The -intercept is . The -intercept is . The -intercept is .
The -intercept is .
The -intercept is .
The -intercept is .
C) The -intercept is . The -intercept is . The -intercept is .
The -intercept is .
The -intercept is .
The -intercept is .
D) The -intercept is . The -intercept is . The -intercept is
.
The -intercept is .
The -intercept is .
The -intercept is .
E) The -intercept is . The -intercept is . The -intercept is .
The -intercept is .
The -intercept is .
The -intercept is .
Write the first-order linear differential equation in standard form.
A)
B)
C)
D)
E)
Find the open intervals on which the function is increasing or
decreasing.
A) The function is increasing on the interval and decreasing on the interval
.
B) The function is increasing on the interval and decreasing on the interval
.
C) The function is increasing on the interval and decreasing on the interval
.
D) The function is increasing on the interval and decreasing on the interval
.
E) The function is increasing on the interval and decreasing on the interval
.
A rectangular page is to contain square inches of print. The margins on each side
are 1 inch. Find the dimensions of the page such that the least amount of paper is used.
A)
B) 15, 15
C) 13, 13
D) 16, 16
E) 14, 14
Use a table of integrals to find the indefinite integral .
A)
B)
C)
D)
E)
Sketch the graph of the relation using any extrema, intercepts, symmetry, and
asymptotes.
A)
B)
C)
D)
E)
An agronomist used four test plots to determine the relationship between the wheat
yield (in bushels per acre) and the amount of fertilizer (in pounds per acre). The
results are shown in the table.
(a) Use the regression capabilities of a graphing utility or a spreadsheet to find the least
squares regression line for the data.
(b) Estimate the yield for a fertilizer application of 160 pounds per acre.
A)
B)
C)
D)
E)
Evaluate the definite integral .
A)
B)
C)
D)
E)
Determine whether is a solution of the differential equation .
A)
B)
C)
D)
E)
Find the center and radius of the sphere whose equation is
. Round your answer to two decimal places,
where applicable.
A) center: ; radius: 2.89
B) center: ; radius: 2.89
C) center: ; radius: 8.35
D) center: ; radius: 2.89
E) center: ; radius: 8.35
Find the exponential function that passes through the two given points
and .
A)
B)
C)
D)
E)
The radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rate of
change of volume when r = 8 inches. Round your answer to one decimal place.
A) 804.2 cubic inches per minute
B) 2144.7 cubic inches per minute
C) 6434.0 cubic inches per minute
D) 2412.7 cubic inches per minute
E) 7238.2 cubic inches per minute
Find the derivative of the following function.
A)
B)
C)
D)
E)
Find the indefinite integral.
A)
B)
C)
D)
E)
Find the radius of convergence of the series .
A) 14
B) 16
C) 1
D) 8
E) 7
Find the period of the trigonometric function.
A)
B)
C)
D)
E)
Find the consumer and producer surpluses by using the demand and supply functions,
where p is the price (in dollars) and x is the number of units (in millions).
Demand Function Supply Function
A) a. $2587.50 b. $3725.00
B) a. $5587.50 b. $4725.00
C) a. $2587.50 b. $1725.00
D) a. $1587.50 b. $4725.00
E) a. $3587.50 b. $4725.00
Find the points of intersection (if any) of the graphs of the equations and
.
A)
B)
C)
D)
E)
Find the derivative of the function .
A)
B)
C)
D)
E)
For the given probability density function, find
A) 12.000
B) 6.400
C) 9.000
D) 5.400
E) 28.800
Find the slope m and y-intercept b of the line whose equation is given below.
A)
B)
C)
D)
E)
A card is chosen at random from three 52-card decks of standard playing cards . What is
the probability that the card will be black and a face card? A face card is a king, a
queen, or a jack.
A)
B)
C)
D)
E)
Apply Taylor’s Theorem to find the power series centered at for the function
.
A)
B)
C)
D)
E)
What is the annual percentage yield (or effective annual rate) for a nominal rate of 8.1%
compounded quarterly?
A) 8.10%
B) 8.41%
C) 8.44%
D) 8.35%
E) 8.26%
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
Find the solution of the differential equation , without solving it.
A)
B)
C)
D)
E)
Differentiate the series for to find the power series for the function .
A)
B)
C)
D)
E)
Find three positive numbers x, y, and z whose sum is 33 and the sum of the squares is a
maximum.
A) x = y = z = 11
B) x = 5.5, y = 5.5, z = 22
C) x = 8.25, y = 8.25, z = 16.5
D) x = 4.4, y = 6.6, z = 11
E) x = 2.2, y = 13.2, z = 17.6
Determine the convergence or divergence of the series.
A) inconclusive
B) diverges
C) converges
Find the mean, variance, and standard deviation of the uniform distribution
over the interval [0, 8] without using integration.
A)
expected value mean : 4.000
variance: 5.333
standard deviation: 2.309
B)
expected value mean : 5.333
variance: 4.000
standard deviation: 2.309
C)
expected value mean : 5.333
variance: 2.309
standard deviation: 4.000
D)
expected value mean : 2.309
variance: 4.000
standard deviation: 5.333
E)
expected value mean : 4.000
variance: 2.309
standard deviation: 5.333
Determine the principal P that must be invested at interest rate r compounded
continuously, so that $1,000,000 will be available for retirement in years ,
.
A) $49787.07
B) $50787.07
C) $49000.04
D) $40000.06