Determine the relative extrema of the function on the interval .
A) relative minimum: relative maximum:
B) relative minimum: relative maximum:
C) relative minimum: relative maximum:
D) relative minimum: relative maximum:
E) relative minimum: relative maximum:
Find the indefinite integral.
A)
B)
C)
D)
E)
Find the slopes of the surface in the x– and y– directions at the point
.
A) slope in x-direction: 2 slope in y-direction: “17
B) slope in x-direction: “6 slope in y-direction: “8
C) slope in x-direction: “17 slope in y-direction: 2
D) slope in x-direction: “14 slope in y-direction: “14
E) slope in x-direction: “8 slope in y-direction: “6
Evaluate the double integral . Round your answer to two
decimal places, where applicable.
A) 69.75
B) 184.25
C) 192.25
D) 191.25
E) 184.75
Find the x-values (if any) at which the function is not continuous.
Which of the discontinuities are removable?
A) continuous everywhere
B) , removable
C) , removable
D) , not removable
E) both B and C
Use the graph of to identify at which of the indicated points the derivative
changes from negative to positive.
A) (2,4)
B) (-1,2)
C) (-1,2), (5,6)
D) (5,6)
E) (2,4), (5,6)
Find the indefinite integral of the following function and check the result by
differentiation.
A)
B)
C)
D)
E) none of the above
The cost C (in millions of dollars) for the federal government to seize p% of a type of
illegal drug as it enters the country is modeled by , for .
Find the limit of C as .
A) 580
B)
C)
D)
E)
Find an equation of the a line that is tangent to the graph of f and parallel to the given
line.
A)
B)
C)
D)
E) both B and D
In 2004, a product has a value of $2875. Over the next five years, its value will increase
by $150 per year. Write a linear equation that gives the dollar value V in terms of the
year t. (Let t = 0 represent 2000.)
A) V = 150t + 2875
B) V = 150t 2875
C) V = 150t + 2275
D) V = 150t + 3475
E) V = 150t 2275
Solve the following equation for accurate to three decimal places.
A)
B)
C)
D)
E)
The population P ( in thousands) of Japan from 1980 through 2010 can be modeled by
where t is the year, with t =0 corresponding to 1980.
Determine the population growth rate, .
A)
B)
C)
D)
E)
Simplify .
A)
B)
C)
D)
E)
Find the slope m and y-intercept b of the line whose equation is given below.
A)
B)
C)
D)
E) Both m and b are undefined.
A survey of high school seniors from a certain school district who took the SAT has
determined that the mean score on the mathematics portion was 650 with a standard
deviation of 13.5. By a normal probability density function the data can be modeled as
. Find the derivative of the model.
A)
B)
C)
D)
E)
Suppose that the numbers W (in thousands) of construction workers employed in the
United States during 2006 can be modeled by where
t is the time in months, with corresponding to January 1. Approximate the month t
in which the number of construction workers employed was a maximum. What was the
maximum number of construction workers employed? Round your answer to nearest
hundredth.
A) July; The maximum number of construction workers employed is 9559.
B) May; The maximum number of construction workers employed is 9539.
C) June; The maximum number of construction workers employed is 9539.
D) May; The maximum number of construction workers employed is 9549.
E) June; The maximum number of construction workers employed is 9549.
Find if .
A)
B)
C)
D)
E)
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)
Write the equation and graph the line that passes through the given point and has the
slope indicated.
with 0 slope
A)
B)
C)
D)
E)
Solve for t. Round your answer to four decimal places.
A) 1.1772
B) 0.2942
C) 2.5673
D) 0.2943
E) 2.4502
Solve the exponential equation. Give the answer correct to 3 decimal places.
A) “0.243
B) 17.028
C) 2.704
D) “17.028
E) “2.173
A baseball fan examined the record of a favorite baseball player’s performance during
his last 50 games. The numbers of games in which the player had zero, one, two, three,
and four hits are recorded in the table shown below. Find the standard deviation .
Round your answer to two decimal places.
A) 1.44
B) 1.12
C) 1.55
D) 1.25
E) 1.20
If the total cost function for a product is dollars. Find the
minimum average cost.
A)
B)
C)
D)
E)
The normal average daily temperature in degrees Fahrenheit for a city is given by
where t is the time in days, with corresponding to January
1. Find the warmest day.
A) March 16
B) March 15
C) April 16
D) April 15
E) April 14
Find the least squares regression line for the points (1,0) , (3,3) , (8,6).
A)
B)
C)
D)
E) none of the above
What are the next three terms in the arithmetic sequence ?
A)
B)
C)
D)
E)
Use Lagrange multipliers to find the minimum distance from the circle
to the point Round your answer to the nearest tenth.
A) 13.6
B) 107.0
C) 184.4
D) 7.8
E) 60.4
Determine the maximum error guaranteed by Taylor’s Theorem with Remainder when
the seventh-degree Taylor polynomial is used to approximate in the interval
centered at 0. Round your answer to five decimal places.
A) 0.02002
B) 0.00202
C) 0.00020
D) 0.00002
E) 0.05002
Find the derivative of
A)
B)
C)
D)
E)
Find the derivative of the function .
A)
B)
C)
D)
E)
Find the sum of the convergent series.
A)
B)
C)
D) 7
E) 1
Find the slope of the tangent line to the graph of the function at the given
point.
A)
B)
C)
D)
E) none of the above
Use a table of integrals to find the indefinite integral .
A)
B)
C)
D)
E)
Given and , evaluate
A) 1
B) 4
C) “60
D) 37
E) 16
Locate any relative extrema and inflection points of the function . Use a
graphing utility to confirm your results.
A) relative maximum value at ; inflection point at x = 0
B) relative minimum value at ; inflection point at x = 0
C) relative minimum value at ; no inflection points
D) relative minimum value at ; no inflection points
E) relative maximum value at ; no inflection points