July 23, 2017

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