July 23, 2017

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)