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