Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
Determine whether y is a function of x.
A) Yes
B) No
Find the cost function for the marginal cost and fixed cost of
(for x = 0).
A)
B)
C)
D)
E)
Integrate the series for to find the power series for the function .
A)
B)
C)
D)
E)
Use a double integral to find the area of the region bounded by the graphs of
and .
A)
B)
C)
D)
E)
Find the limit.
A)
B)
C) 1
D) 0
E) does not exist
The Cobb-Douglas production function for an automobile manufacturer is
where x is the number of units of labor and y is the number of
units of capital. Estimate the average production level if the number of units of labor x
varies between 250 and 300 and the number of units of capital y varies between 250 and
300.
A) 20.99
B) 21.10
C) 10.99
D) 31.44
E) 31.24
Find the points of inflection and discuss the concavity of the function.
A) inflection point at ; concave upward on ; concave downward on
B) inflection point at ; concave downward on ; concave upward on
C) inflection point at ; concave upward on ; concave downward on
D) inflection point at ; concave downward on ; concave upward on
E) none of the above
The cost C (in dollars) of producing x units of a product is given by .
Find the additional cost when the production increases from 9 t o10.
A)
B)
C)
D)
E)
Find the length of each side of the right triangle from the following figure.
A) a 15, b 8, c 17
B) a 8, b 15, c 17
C) a 17, b “8, c 15
D) a 15, b 8, c “17
E) a 15, b 15, c 17
A function and its graph are given. Use the second derivative to locate all x-values of
points of inflection on the graph of . Check these results against the graph
shown.
A)
B)
C)
D) ,
E) , ,
Use Newton’s Method to approximate the zero(s) of the function
accurate to three decimal places.
A) 0.755
B) 0.759
C) “0.755
D) “0.759
E) 0.748
Analytically determine the location of any vertical asymptotes.
A)
B)
C)
D)
E) no vertical asymptotes
After t years, the remaining mass y(in grams) of 20 grams of a radioactive element
whose half-life is 35 years is given by , for . How much of the initial
mass remains after 140 years? Round your answer to two decimal places.
A) 2.50 grams
B) 2.45 grams
C) 3.55 grams
D) 3.40 grams
E) 1.25 grams
Use integration to find a general solution of the differential equation.
A)
B)
C)
D)
E)
Approximate the definite integral “by hand,” using the Trapezoidal Rule with
trapezoids. Round answer to three decimal places.
A) 11.425
B) 11.381
C) 5.691
D) 8.569
E) 15.175
If x is the net gain to a player in a game of chance, then E(x) is usually negative. This
value gives the average amount per game the player can expect to lose over the long
run. A service organization is selling $2 raffle tickets as part of a fundraising program.
The first prize is a boat valued at $2920, and the second prize is a camping tent valued
at $600. In addition to the first and second prizes, there are twenty-two $20 gift
certificates to be awarded. The number of tickets sold is 3000. Find the expected net
gain to the player for one play of the game. Round your answer to the nearest cent.
A) 1178.00
B) 1.47
C) 0.68
D) “$0.68
E) “$1178.00
Both a function and its derivative are given. Use them to find all critical numbers.
A)
B)
C)
D)
E)
Evaluate the double integral .
A)
B)
C)
D)
E)
Solve the equation below for . For some of the equations you should use
the trigonometric identities listed in this section. Use the trace feature of a graphing
utility to verify your results.
A)
B)
C)
D)
E)
Use the properties of logarithms to approximate given that and
A) “6.0088
B) “1.2130
C) 0.6641
D) 8.6586
E) 6.0088
Use a table of integrals with forms involving to find
A)
B)
C)
D)
E)
Use Lagrange multipliers to find the given extremum. In each case, assume that and
are positive.
Maximize Constraint
A)
B)
C)
D)
E)
You are in a boat 2 miles from the nearest point on the coast. You are to go to point Q
located 3 miles down the coast and 1 mile inland (see figure). You can row at a rate of 1
miles per hour and you can walk at a rate of 2 miles per hour. Toward what point on the
coast should you row in order to reach point Q in the least time?
A) 3 miles
B) 8 miles
C) 2 miles
D) 1 mile
E) 5 miles
Which of the following is the correct graph of y = x ” x3?
A)
B)
C)
D)
E)
Examine the function for relative extrema.
A) relative at
B) relative at
C) relative at
D) relative at
E) no relative extrema
Find the absolute extrema of the function on the closed interval .
Round your answer to two decimal places.
A) The maximum of the function is 1 and the minimum of the function is 0.
B) The maximum of the function is 2.92 and the minimum of the function is 1.
C) The maximum of the function is 2.92 and the minimum of the function is 0.
D) The maximum of the function is1 and the minimum of the function is 2.08.
E) The maximum of the function is 0 and the minimum of the function is 2.08.
A brick becomes dislodged from the Empire State Building (at a height of 1025 feet)
and falls to the sidewalk below. Write the position s(t), velocity v(t), and acceleration
a(t) as functions of time.
A) ; ;
B) ; ;
C) ; ;
D) ; ;
E) ; ;
Sketch the graph of the function .
A)
B)
C)
D)
E)
A meteorologist predicts that the amount of rainfall (in inches) expected for a certain
coastal community during a hurricane has the probability density function
. Find and interpret the probability .
A) 90% probability of receiving up to 13 inches of rain
B) 96% probability of receiving up to 13 inches of rain
C) 98% probability of receiving up to 13 inches of rain
D) 4% probability of receiving up to 13 inches of rain
E) 10% probability of receiving up to 13 inches of rain
Use Newton’s Method to approximate . Round your answer to three decimal places.
A) 0.714
B) 1.476
C) 2.597
D) 1.627
E) 2.000
Decide whether the following integral is improper.
A) no
B) yes
Let x represent the units of labor and y the capital invested in a manufacturing process.
When 135,540 units are produced, the relationship between labor and capital can be
modeled by . Find the rate of change of y with respect to x when
.
A) -2
B) 0
C) 3
D) -7
E) 5
Solve the exponential equation. Give the answer correct to 3 decimal places.
A) 0.735
B) 1.471
C) 2.719
D) 1.242
E) 4.970