July 23, 2017

Differentiate the given function.

A)

B)

C)

D)

E)

Let . Determine the following limit. (Hint: Use the graph of the

function.)

A) 5

B) 1

C) 4

D) 16

E) does not exist.

Solve for y in two ways.

A)

B)

C)

D)

E)

Find .

A)

B)

C)

D)

E)

Find the definite integral.

A)

B)

C)

D)

E) none of the above

Write an equation of the line that passes through the point (i) parallel to the given line,

and (ii) perpendicular to the given line.

A) (i) parallel: (ii) perpendicular:

B) (i) parallel: (ii) perpendicular:

C) (i) parallel: (ii) perpendicular:

D) (i) parallel: (ii) perpendicular:

E) (i) parallel: (ii) perpendicular:

Sketch the region whose area is given by the following double integral.

A)

B)

C)

D)

E)

Assume that the number (in millions) of basic cable television subscribers in the United

States from 1996 through 2005 is given in the following table. Use a graphing utility to

graph a scatter plot of the given data. Describe any trends that appear within the last

four years.

A)

The number of subscribers appears to be increasing.

B)

The number of subscribers appears to be decreasing.

C)

The number of subscribers appears to be linearly decreasing.

D)

The number of subscribers appears to be decreasing.

E)

The number of subscribers appears to be linearly increasing.

Find the the distance between the two points and .

A) 1 units

B) 11 units

C) units

D) 3 units

E) 5 units

Use a graphing utility to graph the function . Be sure to choose an

appropriate viewing window.

A)

B)

C)

D)

E)

Suppose that and . Find the following limit:

A) "12

B) "23

C) "1

D) 132

E) 11

Find .

A)

B)

C)

D)

E)

Write the first five terms of the power series .

A)

B)

C)

D)

E)

Find the derivative of the following function.

A)

B)

C)

D)

E)

Use the Ratio Test to determine the convergence or divergence of the series.

A) Ratio Test is inconclusive

B) diverges

C) converges

Evaluate (if possible) the function at the given value of the independent variable.

Simplify the results.

A) 15

B) 3

C) 5

D) "7

E) undefined

Use the properties of logarithms to write the expression as a sum,

difference, or multiple of logarithms.

A)

B)

C)

D)

E)

Find the derivative of the function.

A)

B)

C)

D)

E) none of the above

The number of a certain type of bacteria increases continuously at a rate proportional to

the number present. There are 200 present initially, and 400 present 7 hours later. How

many will there be 20 hours after the initial time? Round your answer to the nearest

integer.

A) 28 bacteria

B) 1344 bacteria

C) 1449 bacteria

D) 41 bacteria

E) 36 bacteria

Evaluate the double integral . Round your answer to two decimal

places, where applicable.

A) 48.50

B) 68.50

C) 49.50

D) 58.50

E) 24.00

Sketch the graph of the probability density function over the interval .

A)

B)

C)

D)

E)

The rate of change of the population of a city is proportional to the population at any

time (in years). In 2000, the population was 200,000, and the constant of proportionality

was 0.015. Estimate the population of the city in the year 2020.

A) 260,972 people

B) 268,972 people

C) 263,972 people

D) 266,972 people

E) 269,972 people

Find the value of the constant a that makes the given function a probability density

function on the stated interval.

A)

B)

C)

D)

E) 1

During a chemical reaction, a compound changes into another compound at a rate

proportional to the unchanged amount . Write the differential equation for the

chemical reaction model. Find the particular solution when the initial amount of the

original compound is 20 grams and the amount remaining after 1 hour is 16 grams.

A)

B)

C)

D)

E)

Find the derivative of the function.

A)

B)

C)

D)

E)

Analyze and sketch a graph of the function .

A)

B)

C)

D)

E)

Find the area of the region bounded by the graphs of the algebraic functions.

A)

B)

C)

D)

E)

Find the least squares regression line for the given points. Then plot the points and

sketch the regression line.

A)

B)

C)

D)

E)

Find the lengths of the sides of the triangle with the given vertices, and determine

whether the triangle is a right triangle, an isosceles triangle, or neither.

A) ; obtuse triangle

B) ; right triangle

C) ; right triangle

D) ; acute triangle

E) ; acute triangle

Describe the interval s on which the function is continuous.

A)

B)

C)

D)

E)

Approximate the integral using Simpson's Rule: , n = 6. Round your

answer to three decimal places.

A) 1.161

B) 1.284

C) 0.850

D) 0.652

E) 1.017

Find any vertical asymptotes for the given function.

A)

B)

C)

D)

E) no vertical asymptotes