July 23, 2017

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