Determine the quadrant in which lies if sin q > 0 and cos q < 0.
A) third quadrant
B) second quadrant
C) fourth quadrant
D) first quadrant
E) first or third quadrants
A point is moving along the graph of the function such that
centimeters per second.
Find dy/dt for the given values of x.
(a) (b)
(a) (b)
A)
B)
C)
D)
E)
You accept a job that pays a salary of 70,000 the first year. During the next 39 years,
you will receive a 6% raise each year. What would be your total compensation over the
40-year period? Round your answer to the nearest integer.
A) 10,833,338
B) 1,166,667
C) 65,800
D) 420,000
E) 4,200
A firm has total revenue given by for x units of a
product. Find the maximum revenue from sales of that product.
A) $1200
B) $914
C) $303
D) $2200
E) $631
Use Simpson’s Rule to approximate the revenue for the marginal revenue function
with n = 4. Assume that the number of units sold, x, increases from
12 to 16. Round your answer to one decimal place.
A) $1602.40
B) $678.36
C) $1346.14
D) $1439.03
E) $1230.54
Use separation of variables to find the general solution of the differential equation.
A)
B)
C)
D)
E)
Find the general solution satisfies the differential equation. Then find the particular
solution that satisfies the initial condition. General Solution:
Differential equation: Initial condition:
A)
B)
C)
D)
E)
Find an equation of the tangent line to the graph of the function at the given point.
A)
B)
C)
D)
E)
The measurement of the edge of a cube is found to be 11 inches, with a possible error of
0.01 inch. Use differentials to estimate the propagated error in computing (a) the
volume of the cube and (b) the surface area of the cube. Give your answers to two
decimal places.
A) 4.36, 1.32
B) 2.90, 1.19
C) 3.27, 1.19
D) 2.90, 1.06
E) 3.63, 1.32
Use a double integral to find the volume of the solid bounded by the graphs of the
equations.
A)
B)
C)
D)
E)
A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at
time distilled water is added to the tank at a rate of 30 gallons per minute, and the
well-stirred solution is withdrawn at the same rate. Find the amount of concentrate Q in
the solution as a function of t.
A)
B)
C)
D)
E)
p is in dollars and q is the number of units. Find the elasticity of the demand function
at the price .
A) “5.40
B) 1.00
C) 5.40
D) “3.00
E) 3.00
This problem contains a function and its graph, where Use the graph to
determine, as well as you can, the horizontal asymptote. Check your conclusion by
using the function to determine the horizontal asymptote analytically.
A)
B)
C)
D)
E)
Find given that and .
A)
B)
C)
D)
E)
Use integration by parts to evaluate
A)
B)
C)
D)
E)
Find the limit:
A) 0
B)
C) 1
D) “1
E)
Evaluate the integral
A)
B)
C)
D)
E)
A Norman window is constructed by adjoining a semicircle to the top of an ordinary
rectangular window (see figure). Find the dimensions of a Norman window of
maximum area if the total perimeter is 24 feet. Round yours answers to two decimal
places.
A) x = 6.72 feet and y = 3.36 feet
B) x = 3.36 feet and y = 7.68 feet
C) x = 2.24 feet and y = 9.12 feet
D) x = 5.72 feet and y = 4.65 feet
E) x = 7.72 feet and y = 2.08 feet
Use a symbolic integration utility to evaluate the double integral.
A) 8.1747
B) 9.1211
C) 6.2031
D) 7.88.7522
E) 9.4362
Identify the open intervals where the function is increasing or
decreasing.
A) decreasing: ; increasing:
B) increasing: ; decreasing:
C) increasing: ; decreasing:
D) increasing: ; decreasing:
E) decreasing for all x
The sum of the length (denote by z) and the girth (perimeter of a cross section) of
packages carried by a delivery service cannot exceed 72 inches. Find the dimensions of
the rectangular package of largest volume that may be sent.
A) x = 9, y = 9, z = 24
B) x = 6, y = 6, z = 48
C) x = 12 , y = 12 , z = 24
D) x = 4.8, y = 7.2, z = 48
E) x = 2.4, y = 14.4, z = 38.4
Determine whether the function is a solution of the differential equation
.
A) Solution
B) Not a solution
Find the slope m and y-intercept b of the line whose equation is given below.
A)
B)
C)
D)
E)
Find the solution of the differential equation , without solving it.
A)
B)
C)
D)
E)
A body assimilates a 12-hour cold tablet at a rate modeled by
where is measured in milligrams per hour
and is the time in hours. Use Simpson’s Rule with to estimate the total amount
of the drug absorbed into the body during the 12 hours.
A) 58.915 mg
B) 68.915 mg
C) 38.915 mg
D) 48.915 mg
E) 78.915 mg
Find the derivative of the following function.
A)
B)
C)
D)
E)
Find .
A) 3
B) inf
C) 0
D) “3
E)
Use the Midpoint Rule n = 4 to approximate the area of the following region.
A) 2.5
B) 1.2
C) 1.5
D) 1.9
E) 2.3
The demand function for a product is , where p is the number of dollars
and x is the number of units. If the equilibrium price is , what is the consumer’s
surplus?
A) $
B) $
C) $
D) $
E) $
Find the derivative of the trigonometric function.
A)
B)
C)
D)
E)
From the given function , find the following trigonometric function.
A)
B)
C)
D)
E)
Find the derivative of the function .
A)
B)
C)
D)
E)
Find the constant k such that the function is a probability density function
over the interval .
A) 5
B)
C)
D)
E)
Find the average value of the function over the given interval.
on [-3,3]
A) 15
B) 52.5
C) 90
D) 10
E) 50
Find any critical numbers of the function , t < 5.
A) 0
B)
C)
D) both A and B
E) both A and C