July 23, 2017

Evaluate the integral .

A)

B)

C)

D)

E)

Determine the convergence or divergence of the following series.

A) converges

B) diverges

Determine whether y is a function of x.

A) Yes

B) No

Use the advertising awareness model described to find the number of people y (in

millions) aware of the product as a function of time t (in years). when ;

when

A)

B)

C)

D)

E)

Find the x- and y- intercepts of the graph of the equation .

A) x-intercepts: , ; y-intercepts:

B) x-intercepts: , ; y-intercepts:

C) x-intercepts: , ; y-intercepts: ,

D) x-intercepts: , ; y-intercepts: ,

E) x-intercept: ; y-intercept:

When the price of a glass of lemonade at a lemonade stand was $1.75, 400 glasses were

sold. When the price was lowered to $1.50, 500 glasses were sold. Assume that the

demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,

respectively. Find the marginal profit when 300 glasses of lemonade are sold and when

700 glasses of lemonade are sold.

A)

B)

C)

D)

E)

Find the extrema of the function by analyzing its graph below.

A) (0, 1)

B) no relative extrema

C) , (0, 0)

D)

E)

Use Newton's Method to approximate the zero(s) of the function

accurate to three decimal places.

A) 16.944

B) 16.948

C) "16.944

D) "16.948

E) 16.938

Use this equation and Find for each situation. (a)

(b)

A) a. 685099.00 b. 5802815.12

B) a. 585099.00 b. 5802815.12

C) a. 685099.00 b. 6802815.12

D) a. 585099.00 b. 4802815.12

E) a. 485099.00 b. 5802815.12

Use the values and to evaluate the definite integral

.

A) 21

B) "9

C) 1

D) 11

E) "7

Write the first five terms of the sequence of partial sums.

A)

B)

C)

D)

E)

The profit (in dollars) from selling x units of calculus textbooks is given by

. Find the marginal profit when . Round your answer

to two decimal places.

A) $34.80

B) $864.80

C) $5.20

D) $20.00

E) $859.55

Use Newton's Method to approximate the x-value of the indicated point intersection of

the two graphs accurate to three decimal places.

A) 0.371

B) 0.363

C) 0.356

D) 0.359

E) 0.352

Identify the quadric surface.

A) The graph is a hyperboloid of one sheet.

B) The graph is hyperboloid of two sheets.

C) The graph is an elliptic cone.

D) The graph is an elliptic paraboloid.

E) The graph is an ellipsoid.

Determine the dimensions of a rectangular solid (with a square base) with maximum

volume if its surface area is 361 square meters.

A) square base side ; height

B) square base side ; height

C) square base side ; height

D) square base side ; height

E) square base side ; height

Identify the open intervals where the function is increasing or

decreasing.

A) increasing: ; decreasing:

B) decreasing: ; increasing:

C) increasing on

D) decreasing on

E) none of the above

Find the derivative of the function.

A)

B)

C)

D)

E)

The profit P (in thousands of dollars) for a company spending an amount s (in

thousands of dollars) on advertising is The point of

diminishing returns is the point at which the rate of growth of the profit function begins

to decline. Find the point of diminishing returns. Round your answer to the nearest

thousand dollars.

A) 40 thousand dollars

B) 120 thousand dollars

C) 96 thousand dollars

D) 160 thousand dollars

E) 80 thousand dollars

Some of the curves corresponding to different values of C in general solution of the

differential equation are shown in the figure given below. Find the

particular solution that passes through the points plotted on the graph.

A)

B)

C)

D)

E)

Bouncing Ball. A ball dropped from a height of 38 feet bounces to of its former

height with each bounce. Find the total vertical distance that the ball travels.

A) 266 feet

B) 304 feet

C) 146 feet

D) 104 feet

E) 152 feet

Find the indefinite integral.

A)

B)

C)

D)

E)

Write the first five terms of the sequence.

an =

A)

B)

C)

D)

E) none of the above

Let be a random variable that is normally distributed with the given mean and

standard deviation . Find the probability using a symbolic integration

utility. Round your answer to four decimal places.

A) 0.1908

B) 0.3085

C) 0.2525

D) 0.1695

E) 0.0763

Find the market equilibrium point for the following demand and supply functions

below, where p is price per unit and q is the number of units produced and sold.

Demand: Supply:

A)

B)

C)

D)

E)

A wet towel hung from a clothesline to dry loses moisture through evaporation at a rate

proportional to its moisture content. After 1 hour, the towel has lost 40% of its original

moisture content. How long will it take the towel to lose 80% of its original moisture

content?

A) 2.15

B) 4.95

C) 3.95

D) 3.15

E) 4.15

Find the standard equation of the sphere whose center is and whose radius is

4.

A)

B)

C)

D)

E)

If find .

A)

B)

C)

D)

E)

Use the given information to find of the function .

A)

B)

C)

D)

E)

Find the area between the curve and the x-axis from .

A)

B)

C)

D)

E)

Determine whether the given function is continuous. If it is not, identify where it is

discontinuous.

A) discontinuous at

B) discontinuous at

C) discontinuous at

D) discontinuous at

E) continuous everywhere

Estimate the variance for the following probability distribution to two decimal places.

A)

B)

C)

D)

E) 1.00

Use a double integral to find the volume of the indicated solid.

A)

B)

C)

D)

E) none of the above