July 23, 2017

Evaluate the integral

A)

B)

C)

D)

E)

Find constants a and b such that the function

is continuous on the entire real line.

A) a = 3 , b = 0

B) a = 3 , b = "3

C) a = 3 , b = 3

D) a = "3 , b = 3

E) a = "3 , b = "3

Use the Midpoint Rule with to approximate where . Then use a

graphing utility to evaluate the definite integral. Compare your results.

A) a. Midpoint Rule: b. Graphing utility:

B) a. Midpoint Rule: b. Graphing utility:

C) a. Midpoint Rule: b. Graphing utility:

D) a. Midpoint Rule: b. Graphing utility:

E) a. Midpoint Rule: b. Graphing utility:

Profit. Suppose that the monthly revenue and cost (in dollars) for x units of a product

are At what rate per month is the profit changing if

the number of units produced and sold is 100 and is increasing at a rate of 10 units per

month?

A) per month

B) per month

C) per month

D) per month

E) per month

Use the product Rule to find the derivative of the function .

A)

B)

C)

D)

E)

Describe the interval(s) on which the function is continuous.

A) and

B) and

C) and

D)

E) none of these choices

Use the properties of exponents to simplify the expression .

A)

B)

C)

D)

E)

Find if .

A)

B)

C)

D)

E)

Find the indefinite integral.

A)

B)

C)

D)

E)

Analytically determine the location(s) of any vertical asymptote(s).

A)

B)

C) ,

D)

E) no vertical asymptotes

Find the second derivative of the function .

A)

B)

C)

D)

E)

A function and its graph are given. Use the graph to find the vertical asymptotes, if they

exist. Confirm your results analytically.

A)

B)

C)

D)

E) no vertical asymptotes

At any time (in years), the rate of growth of the population of deer in a state park is

proportional to the product of and , where is the maximum number of

deer the park can maintain. (a) Use a symbolic integration utility to find the general

solution. (b) Find the particular solution given the conditions when and

when (c) Find when (d) Find when

A) a. b. c. 121 deer d.

B) a. b. c. 121 deer d.

C) a. b. c. 121 deer d.

D) a. b. c. 131 deer d.

E) a. b. c. 121 deer d.

Use the rectangles to approximate the area of the region. Compare your result with the

exact area obtained with a definite integral.

A) a. The approximate area: 3 b. The exact area: 2

B) a. The approximate area: 2 b. The exact area: 3

C) a. The approximate area: 2 b. The exact area: 1

D) a. The approximate area: 2 b. The exact area: 2

E) a. The approximate area: 1 b. The exact area: 2

Use a graphing utility to graph the function .

A)

B)

C)

D)

E)

Sketch the graph of the function .

A)

B)

C)

D)

E)

Find the derivative of the function .

A)

B)

C)

D)

E)

Find the Taylor polynomials (centred at zero) of degree (a) 1, (b) 2, (c) 3, and (d) 4.

A)

B)

C)

D)

E)

Approximate the value of the definite integral using (a) the Trapezoidal Rule and (b)

Simpson's Rule for the indicated value of n. Round your answers to three significant

digits.

A) a. Trapezoidal Rule: b. Simpson's Rule:

B) a. Trapezoidal Rule: b. Simpson's Rule:

C) a. Trapezoidal Rule: b. Simpson's Rule:

D) a. Trapezoidal Rule: b. Simpson's Rule:

E) a. Trapezoidal Rule: b. Simpson's Rule:

Use the graph of to sketch y = .

A)

B)

C)

D)

E)

Write the the differential equation by separating the variables.

A)

B)

C)

D) No, the variables cannot be separated

E)

Find the radius of convergence of the series .

A) 1

B) 4

C) 6

D) 8

E) 5

Find the indefinite integral of the following function and check the result by

differentiation.

A)

B)

C)

D)

E) none of the above

The integrand of the following definite integral is a difference of two functions.

Sketch the graph of the two functions and shade the region whose

area is represented by the integral.

A)

B)

C)

D)

E)

Find .

A)

B)

C)

D)

E)

If the total cost function for a product is dollars, determine

how many units x should be produced to minimize the average cost per unit?

A) 149 units

B) 500 units

C) 91 units

D) 129 units

E) 81 units

The two planes and are parallel.

A) true

B) false

Find the limit of the following sequence.

A)

B)

C)

D)

E) The sequence diverges.

Evaluate the integral .

A)

B)

C)

D)

E)

Find any horizontal asymptotes for the given function.

A)

B)

C)

D)

E) no horizontal asymptotes

Use the initial condition to find the particular solution of the differential equation.

, when

A)

B)

C)

D)

E)

Determine the convergence or divergence of the p-series .

A) The series diverges.

B) The series converges.

Find an equation of the line that passes through the point ("6,12) and has the slope m

that is undefined.

A) y = "6

B) x = "6

C) y = 12

D) x = 12

E) y = "6x

Find given the probability distribution.

A) 0.159

B) 0.797

C) 0.203

D) 0.956

E) 0.044

Find the expected value for the following probability distribution. Round your

answer to three decimal places.

A) 7.225

B) 904.398

C) 2,724.840

D) 817,935.160

E) 52.200

A publishing company introduces a new weekly magazine that sells for $4.69 on the

newsstand. The marketing group of the company estimates that sales x (in thousands)

will be approximated by the following probability function. Find the expected revenue.

Round your answer to the nearest dollar.

A) 93,565

B) 94

C) 456

D) 19,950

E) 456,091

An insurance company needs to determine the annual premium required to break even

on fire protection policies with a face value of 90,000. If x is the claim size on these

policies and the analysis is restricted to the losses 30,000, 50,000, and 90,000,

then the probability distribution of x is as shown in the table. What premium should

customers be charged for the company to break even? Round your answer to the nearest

dollar.

A) 553

B) 24

C) 42,500

D) 558

E) 62,000

Complete the table for the function . Let x = 4.

4.00000

2.00000

0.40000