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Find the derivative of the function.
A)
B)
C)
D)
E) none of the above
Find the x-values (if any) at which the function is not continuous. Which
of the discontinuities are removable?
A) 2 and -2, not removable
B) continuous everywhere
C) 2 and -2, removable
D) discontinuous everywhere
E) none of the above
The daily demand for a certain product (in hundreds of pounds) is a random variable
with the probability density function over the interval . Find
the probability that is within one standard deviation of the mean. Express your
answer as a percent.
A) 96.37
B) 49.27
C) 62.61
D) 13.34
E) 72.72
Find the equation of the function whose derivative is and whose
graph passes through the point .
A)
B)
C)
D)
E)
A rancher has 520 feet of fencing to enclose two adjacent rectangular corrals (see
figure). What dimensions should be used so that the enclosed area will be a maximum?
A) and
B) and
C) and
D) and
E) and
The effective yield is the annual rate i that will produce the same interest per year as the
nominal rate compounded n times per year. For a rate that is compounded n times per
year, the formula for effective yield is given as . Find the effective yield
for a nominal rate of 6%, compounded monthly. Round your answer to two decimal
places.
A) 0.62%
B) 6.41%
C) 6.80%
D) 1.18%
E) 6.17%
Determine the amount of money required to set up a charitable endowment that pays
the amount each year indefinitely for the annual interest rate compounded
continuously.
A) $210,000
B) $200,000
C) $220,000
D) $240,000
E) $230,000
Find the particular solution of the differential equation that satisfies
the boundary condition .
A)
B)
C)
D)
E)
Simplify
A)
B)
C)
D)
E)
Locate the absolute extrema of the function on the closed interval
[0,5].
A) absolute max: f(5) = 65 ; absolute min: f(2) = "16
B) absolute max: f(2) = "16 ; absolute min: f(5) = 65
C) absolute max: f(5) = 65 ; no absolute min
D) no absolute max; absolute min: f(5) = 65
E) no absolute max or min
Write an expression for the nth term of the sequence 2, 8, 26, 80, ....
A)
B)
C)
D)
E)
Sketch the graph of the function .
A)
B)
C)
D)
E)
Use the demand function to find the rate of change in the demand
x for the given price . Round your answer to two decimal places.
A) 26.53 units per dollar
B) "6.63 units per dollar
C) 6.63 units per dollar
D) 36.11 units per dollar
E) "26.53 units per dollar
The measurement of the circumference of a circle is found to be 43 centimeters, with a
possible error of 0.9 centimeters. Approximate the percent error in computing the area
of the circle.
A) 4.65 %
B) 2.09 %
C) 4.19 %
D) 8.37 %
E) 2.33 %
Find the indefinite integral of the following function and check the result by
differentiation.
A)
B)
C)
D)
E) none of the above
Sketch the yz-trace of the equation:
A)
B)
C)
D)
E)
Which of the following is a solution of the differential equation ?
A)
B)
C)
D)
E)
Find the domain and range of the function.
A) Domain: all point such that Range:
B) Domain: all point such that Range:
C) Domain: all point such that Range:
D) Domain: all point such that Range:
E) Domain: all point such that Range:
Describe the trace of the surface given by the function below in the xy-plane.
A) circle
B) ellipse
C) parabola
D) hyperbola
E) line
You deposit 4000 in an account with an annual interest rate of change r (in decimal
form) compounded monthly. At the end of 4 years, the balance is .
Find the rates of change of A with respect to r when .
A) 6709.32
B) 318,595.99
C) 559.11
D) 26549.67
E) 26,265.13
Suppose the resident population P(in millions) of the United States can be modeled by
, where
corresponds to 1800. Analytically find the minimum and maximum populations in the
U.S. for .
A) The population is minimum at and maximum at .
B) The population is minimum at and maximum at .
C) The population is minimum at and maximum at .
D) The population is minimum at and maximum at .
E) The population is minimum at and maximum at .
The two planes and are perpendicular.
A) false
B) true
Evaluate the definite integral.
A)
B)
C) 0
D) 4
E) undefined
The value of an investment of $18,000 after t years in an account for which the
interest rate 100r% is compounded continuously is given by the function
dollars. Write the partial derivative
A)
B)
C)
D)
E)
Find the equation of the sphere that has the points and as endpoints of
a diameter.
A)
B)
C)
D)
E)
Boat docking. Suppose that a boat is being pulled toward a dock by a winch that is 21 ft
above the level of the boat deck. If the winch is pulling the cable at a rate of 23 ft/min,
at what rate is the boat approaching the dock when it is 28 ft from the dock? Use the
figure below.
A)
B)
C)
D)
E)
Use the limit definition to find the slope of the tangent line to the graph of
at the point .
A)
B)
C)
D)
E)
Find all relative extrema of the function . Use the Second Derivative
Test where applicable.
A) relative max: f(1) = "6
B) relative min: f(0) = "7
C) no relative max or min
D) both A and B
E) none of the above
Analyze and sketch a graph of the function .
A)
B)
C)
D)
E) none of the above
This problem contains a function and its graph, where Use the graph to
determine, as well as you can, the vertical asymptote. Check your conclusion by using
the function to determine the vertical asymptote analytically.
A)
B)
C)
D)
E) no vertical asymptote
Solve the equation for . For some of the equations you should use the
trigonometric identities listed in this section. Use the trace feature of a graphing utility
to verify your results.
A)
B)
C)
D)
E)
Find the derivative of the following function.
A)
B)
C)
D)
E)
Find the derivative of the following function.
A)
B)
C)
D)
E)
Find the first partial derivatives with respect to x, y, and z.
A)
B)
C)
D)
E)
Find the general solution of the first-order linear differential equation.
A)
B)
C)
D)
E)
