Find the length and width of a rectangle that has perimeter meters and a maximum
area.
A) 1, 3
B) 1, 3
C) 2, 2
D) 3, 1
E) 6, “2
Evaluate the integral .
A)
B)
C)
D)
E)
The management of a factory finds that the maximum number of units a worker can
produce in a day is 30. The learning curve for the number of units N produced per day
after a new employee has worked days is modeled by After 20 days on
the job, a worker is producing 19 units in a day. How many days should pass before this
worker is producing 25 units per day?
A) about 36 days.
B) about 45 days.
C) about 30 days.
D) about 10 days.
Locate any relative extrema and inflection points of the function .
A) no relative extrema; inflection point at
B) relative maximum at ; inflection point at
C) relative minimum at ; inflection point at
D) no relative extrema; inflection point at
E) relative minimum at ; no inflection points
Find the center and radius of the sphere.
A) Center: Radius:
B) Center: Radius:
C) Center: Radius:
D) Center: Radius:
E) Center: Radius:
Find the differential dy of the function .
A)
B)
C)
D)
E)
A store manager wants to know the demand y for an energy bar as a function of price x.
The daily sales for three different prices of the energy bar are shown in the table.
Price, x $ 1.00 $ 1.25 $ 1.54 Demand, y 450 335 300
(i) Use the regression capabilities of a graphing utility to find the least squares
regression line for the data.
(ii) Use the model to estimate the demand when the price is $1.39.
Price, x $ 1.00 $ 1.25 $ 1.54
Demand, y 450 335 300
A) (i) ; (ii) 357.97832
B) (i) ; (ii) “436.133926
C) (i) ; (ii) 525.880529
D) (i) ; (ii) “436.133926
E) none of the above
A business has a cost (in dollars) of for producing x units. What is the
limit of as x approaches infinity?
A)
B) $0.90
C) $400.90
D) $400.00
E) $399.10
Find the speed v, in miles per hour, that will minimize costs on a 105-mile delivery trip.
The cost per hour for fuel is dollars, and the driver is paid dollars per
hour. (Assume there are no costs other than wages and fuel.)
A) 595 mph
B) 105 mph
C) 700 mph
D) 70 mph
E) 35 mph
Identify u and dv for finding the integral using integration by parts. dx
A) dx; dx
B)
C)
D)
E)
Evaluate the function at
A)
B)
C)
D)
E)
Compare dy and for at x = 1 with dx = 0.05. Give your answers to four
decimal places.
A)
B)
C)
D)
E)
Find the indefinite integral.
A)
B)
C)
D)
E)
Solve the following equation for accurate to three decimal places.
A)
B)
C)
D)
E)
Estimate the surface area of the oil spill shown in the figure using the Midpoint Rule.
A) 481.6
B) 301.6
C) 311.6
D) 431.6
E) 381.6
Sketch the region whose area is given by the definite integral and then use a geometric
formula to evaluate the integral.
A) “318
B) 636
C) 336
D) 168
E) 12
Find the limit: .
A)
B)
C) 0
D) “1
E) 1
Set up an integral for both orders of integration, and use the more convenient order to
evaluate the integral below over the region R.
A)
B)
C)
D)
E)
Find three positive numbers x, y, and z whose sum is 15 and product is a maximum.
A) x = 2.5, y = 2.5, z = 10
B) x = y = z = 5
C) x = 3.75, y = 3.75, z = 7.5
D) x = 2, y = 3, z = 5
E) x = 1, y = 6, z = 8
Solve the exponential equation. Give answers correct to 3 decimal places.
A) 216
B) 0.571
C) 0.774
D) 0.371
E) 108
Find the x-value at which the absolute minimum of f (x) occurs on the interval [a, b].
A)
B)
C)
D)
E)
Write an expression for the nth term of the sequence.
A)
B)
C)
D)
E)
Sketch the graph of the function using any extrema, intercepts,
symmetry, and asymptotes.
A)
B)
C)
D)
E)
Find the radius of convergence of the series .
A) 14
B) 5
C) 1
D) 9
E) 8
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. What is the minimum average cost?
A) $0
B) $10
C) $100
D) $50
E) $505
Find the power series for the function using the power series for .
A)
B)
C)
D)
E)
The graph of the derivative of a function is given below. Sketch the graphs of two
functions that have the given derivative.
A)
B)
C)
D)
E)
Find the indefinite integral.
A)
B)
C)
D)
E)
Express the value of the given repeating decimal as a fraction. [Hint: Write as an
infinite series.]
A)
B)
C)
D)
E)
If
A)
B)
C)
D)
E)
For , find all values of x and y such that and
simultaneously.
A)
B)
C) (0,0)
D) Both B and C
E) Both A and B
Find the particular solution that satisfies the initial condition. ; Initial
Condition: when
A)
B)
C)
D)
E)