Evaluate the integral
A)
B)
C)
D)
E)
Consider the sequence (An) whose nth term is given by Anwhere P is the
principal, An is the amount of compound interest after n months, and r is the annual
percentage rate. Write the first four terms of the sequence for P = 9,500 and r = 0.04.
Round your answer to two decimal places.
A) 9531.67, 9573.51, 9620.26, 9627.30
B) 9532.67, 9573.51, 9620.26, 9660.34
C) 9531.67, 9563.44, 9595.32, 9627.30
D) 9532.67, 9573.51, 9595.32, 9627.30
E) 9532.67, 9563.44, 9595.32, 9660.34
Use a symbolic differentiation utility to find the fourth-degree Taylor polynomials
(centred at zero) .
A)
B)
C)
D)
E)
Find the slope of the line passing through the given pair of points.
and
A)
B) 1
C) “11
D)
E) The slope is undefined.
Graph the function with a graphing utility and use it to predict the limit. Check your
work either by using the table feature of the graphing utility or by finding the limit
algebraically.
A)
B)
C)
D) 0
E) does not exist
Use a change-of-base formula to rewrite the logarithm in terms of natural logarithms.
A)
B)
C)
D)
E)
Find an equation of the tangent line to the graph of at the point .
A)
B)
C)
D)
E) none of the above
Find all relative maxima of the given function.
A)
B)
C)
D) ,
E) no relative maxima
Write the general form of the equation of the circle with endpoints of a diameter at
and .
A)
B)
C)
D)
E)
Find the indefinite integral of the following function.
A)
B)
C)
D)
E)
A firm’s weekly profit (in dollars) in marketing two products is given by
where and represent the numbers of
units of each product sold weekly. Estimate the average weekly profit when varies
between 40 and 50 units and varies between 45 and 50 units.
A)
B)
C)
D)
E)
A population of bacteria is introduced into a culture. The number of bacteria P can be
modeled by where t is the time (in hours). Find the rate of change
of the population when t = 2.
A)
B)
C)
D)
E)
With an annual rate of inflation of 4% over the next 10 years, the approximate cost of
goods or services during any year in the decade is given by
where is the time (in years) and is the present cost. The price of an oil change for a car
is presently $24.95.Estimate the price 10 years from now.
A) $37.09
B) $36.93
C) $89.00
D) $63.90
Sketch the level curves for the function below for the given values .
A)
B)
C)
D)
E)
For the given function, find the relative minima.
A)
B)
C)
D)
E) no relative minima
A business is expected to yield a continuous flow of profit at the rate of $1,000,000 per
year. If money will earn interest at the nominal rate of 8% per year compounded
continuously, what is the present value of the business forever?
A) $12,600,000
B) $12,510,000
C) $12,500,000
D) $1,250,000
E) $1,350,000
Find the marginal cost for producing x units. (The cost is measured in dollars.)
A)
B)
C)
D)
E)
Find the integral below using an integral table.
A)
B)
C)
D)
E)
Find the particular solution of the differential equation passing through
the point .
A)
B)
C)
D)
E)
Evaluate the definite integral of the algebraic function.
Use a graphing utility to verify your results.
A) “6
B) “6
C) 13
D) 18
E) “3
Use the Ratio Test to determine the convergence or divergence of the series
.
A) The series converges.
B) The series diverges.
A calf that weighs 80 pounds at birth gains weight at the rate where
w is weight in pounds and t is time in years. Use a computer algebra system to solve the
differential equation for .
A)
B)
C)
D)
E)
Find the indefinite integral of .
A)
B)
C)
D)
E)
Find the cosine of .
A)
B)
C)
D)
E)
Find the derivative of the function and simplify your answer by using the trigonometric
identities
A)
B)
C)
D)
E)
Find all relative extrema of the function . Use the Second-Derivative
Test when applicable.
A) The relative minimum is and the relative maximum is .
B) The relative maximum is .
C) The relative minimum is .
D) The relative maximum is and the relative minima are and .
E) The relative minimum is and the relative maximum is .
Determine the continuity of the function below.
A) discontinuous at x = 0
B) continuous on the entire real number line
C) discontinuous at x = 1
D) discontinuous at x = 2
E) discontinuous at x = 4
Find the equation of the function f whose graph passes through the point and
whose derivative is .
A)
B)
C)
D)
E)
Future value. The future value that accrues when $500 is invested at 5%, compounded
continuously, is , where t is the number of years. At what rate is the
money in this account growing when
A) $7.10 per year
B) $26.81 per year
C) $709.53 per year
D) $517.81 per year
E) $35.48 per year
Find two values of q that satisfy the equation below. Give values of q in radians
. Do not use a calculator. cos q =
A)
B) ,
C)
D)
E)
Find the derivative of the function .
A)
B)
C)
D)
E)
Find an equation of the tangent line to the graph of f at the given point.
at
A)
B)
C)
D)
E)
Evaluate the following integral.
A)
B)
C)
D)
E) none of the above